Angles and intersecting lines
Angles with triangles and polygons
None
Sum of the exterior angles of convex polygon
More elegant way to find the sum of the exterior angles of a convex polygon
Discussion and questions for this video
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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Is 360 degrees for all polygons ?
Nope! As Sal told at 3:25 it will work for any Convex Polygon, it is clear theat it is only liable for Convex Polygons. Notice, he didn't said that is for all polygons. So don' t get confused with Convex Polygon and all polygon.........
Hope this will help you out of this!
Hope this will help you out of this!
Yes, it is always!
Yes that whats my dad said
Imagine punching a side in on a polygon to form a concave polygon, one with an inverted side, from a convex polygon.
No, only for convex polygon. Here's how you figure it out: draw a line segment starting and ending inside the polygon. If the line crosses over any space not filled by the polygon it's concave. Other wise it's convex.
The sum of all external angles on a polygon = 360 degrees. Kind of like in triangles all interior angles = 180 degrees. ;)
convex polygons... and triangles (i like triangles!)
Imagine that a polygon is nothing more than a incomplete circle.
Yes the sum of the exterior angles of a CONVEX POLYGON equals 360 degrees
Yes, the sum of all exterior angels of a convex polygon is 360 deg, And what's the logic behind this is explained in the video.
"Sum of the exterior angles of CONVEX polygon:"
A basic way of finding the measure of interior angles of a convex polygon: Multiply 180 by the number of sides of the polygon, then subtract 360
Yes, but only for convex polygons
no. different polygons have different sides . that's according to no. of sides they have.
yes it is,as u can see on video
no, a triangle is 180 degrees, pentagon is 540 degrees, a hexagon is 720 degrees. You can find out how many degrees of a polygon by using this. n as amount of sides.
(n2)*180
(n2)*180
JUST CONVEX POLYGONS!
yes for all pOlygons lol
for all convex polygons
yes
yes
I was confused by the definition of "exterior angles".
If the interior angle of one corner is, say, 90 degrees (like a corner in a square) then shouldn't the exterior angle be the whole outside of the angle, such as 270? Why is only 90 degrees counted for the exterior angle of a corner instead of 270?
In other words, exterior corners look like they are always greater than 180, but we subtract the 180. Why?
If the interior angle of one corner is, say, 90 degrees (like a corner in a square) then shouldn't the exterior angle be the whole outside of the angle, such as 270? Why is only 90 degrees counted for the exterior angle of a corner instead of 270?
In other words, exterior corners look like they are always greater than 180, but we subtract the 180. Why?
As I think about this now, it makes sense:
You can think of exterior angles as how many degrees you need to turn at each corner if you're tracing the line around the polygon.
When you walk around the block, you turn 90° at each corner, not 270°. The same applies for any shape. If you were to walk around a hexagon, you would turn only 60° at each corner.
You can think of exterior angles as how many degrees you need to turn at each corner if you're tracing the line around the polygon.
When you walk around the block, you turn 90° at each corner, not 270°. The same applies for any shape. If you were to walk around a hexagon, you would turn only 60° at each corner.
It's just the way exterior angles are defined.
From the wikipedia article: "an exterior angle (or external angle) is an angle formed by one side of a simple, closed polygon and a line extended from an adjacent side."
See: http://en.wikipedia.org/wiki/Exterior_angle
From the wikipedia article: "an exterior angle (or external angle) is an angle formed by one side of a simple, closed polygon and a line extended from an adjacent side."
See: http://en.wikipedia.org/wiki/Exterior_angle
because just is that true
How do you find the exterior angles of a conCAVE polgon, then?
Actually, it is 360°, according to http://en.wikipedia.org/wiki/Exterior_angle
The measure of an interior angle plus the measure of its exterior angle is equal to 180 degrees. So if you have a polygon that has in angle that is 200 degrees, what is it's exterior angle? Well let's see, 200 plus what is equal to 180? 20! But negative angles aren't possible...
Using negative exterior angles might get the sum to 360 in some cases, but don't rely on them  they defy logic!
Using negative exterior angles might get the sum to 360 in some cases, but don't rely on them  they defy logic!
What! There are TWO reflex angles for conCAVE polygons.
Can you have a negative angle?
Yes, if you say that angles measured counterclockwise are positive and those measured clockwise are negative : )
No, angles are defined as being between 0 and 360.
In a polygon with n sides at what point does n+1 equal a circle?
A circle is not a polygon. Polygons are composed of straight sides. A circle does not have straight sides, it has curving sides.
if n is a number of sides, n + 1 cannot be a shape
The more sides a convex polygon, (with sides equal in length), the more it will look like a circle. Therefore, is a circle a polygon with 360 sides which would be equal to sides/points?
Stated another way 
Since there is no theoretical limit to a polygon at what point does the circumcircle of a polygon equal a circle? If so, is a circle a polygon?
Stated another way 
Since there is no theoretical limit to a polygon at what point does the circumcircle of a polygon equal a circle? If so, is a circle a polygon?
A polygon must have straight sides. It cannot have curving sides. However, as you have shown, a curved side can be made from an infinite amount of straight sides. Combining this together there are only two logical conclusions that I can think of. One, a polygon cannot have an infinite amount of sides. It can have 10 sides. It can have 10 million sides. It can have a million million sides. But it cannot have infinity sides. The other logical conclusion is that infinity sides does not make a curve ( I have no argument to back this up ).
An infinite number of sides will *not* make a curve. It only appears to make a curve due to our ability to differentiate things. However, if you are able to look at the sides at the proper scale there would be no question about whether you were looking at a figure that had sides.
Think about viewing things with an electron microscope. They look very different from when you view them with the naked eye. Moving toward the other end of the spectrum, think about how we perceive things when we stand on the earth; it seems "flat" to us when we know that it is actually curved.
In the world of mathematics there is the ability to get infinitely small or infinitely large. So, it is possible to view things at whatever scale is needed to be able to detect the difference.
A circle is not a polygon and never will be. A circle is the collection of all points that are equidistant from a central point. A polygon will never meet that definition.
Think about viewing things with an electron microscope. They look very different from when you view them with the naked eye. Moving toward the other end of the spectrum, think about how we perceive things when we stand on the earth; it seems "flat" to us when we know that it is actually curved.
In the world of mathematics there is the ability to get infinitely small or infinitely large. So, it is possible to view things at whatever scale is needed to be able to detect the difference.
A circle is not a polygon and never will be. A circle is the collection of all points that are equidistant from a central point. A polygon will never meet that definition.
In the example in the video, would the answer be 360 degrees? If so would it always be 360 degrees? If not what would the answer be and how can you find it?
Yes, the answer is 360 degrees and will always be 360 degrees for any convex polygon. Good job on figuring that out!
yes all polygons have an external measure of 360 degrees
is a star considered as a convex polygon?
Wait a minute... A star is both right? Because it is going inward and outward right?
No, it is concave because it has an angle greater than 180 degrees( also known as a reflex angle.
what is a convex polygon?
A convex polygon is a polygon in which no line containing a side of the polygon intersects the interior of the polygon.
It's opposite would be a concave polygon, where a line containing one side of the polygon DOES intersect the interior of the polygon.
It's opposite would be a concave polygon, where a line containing one side of the polygon DOES intersect the interior of the polygon.
a concave polygon goes in on itself but a convex polygon doesn't
A convex polygon is a polygon with no angles that have a measure greater than or equal to 180.
What is the meaning of anticlockwise?
it is the same as counterclockwise, which is the opposite of the direction the hands of a clock go.
Or if you start at the top of a circle, and go down and around to the left.
Or if you start at the top of a circle, and go down and around to the left.
At 3:10 Sal said something like clockwise and counterclockwise..
What does he mean by clockwise and counterclockwise ?
What does he mean by clockwise and counterclockwise ?
Clockwise on the clock rotation goes as toprightdownleft.
Counterclockwise on the clock rotation goes as topleftdownright.
Most clocks go Clockwise.
Counterclockwise on the clock rotation goes as topleftdownright.
Most clocks go Clockwise.
Why didn't Sal define convex?
3:29 Oh wait, never mind...
From now on, I think I'll wait until the end of the video before commenting.
From now on, I think I'll wait until the end of the video before commenting.
always wait until the end of the video to ask a question.
yeah man you should wait
What does he mean by clockwise and counterclockwise ?
It's the way the hands on an analog clock move. if you have a line segment from the center of a circle going straight up, when it moves to the right going on all the way around however far that is clockwise, if it goes left that is counterclockwise.
What is the difference between convex and concave shapes ?
"Convex and Concave Polygons. Every polygon is either convex or concave. The difference between convex and concave polygons lies in the measures of their angles. For a polygon to be convex, all of its interior angles must be less than 180 degrees."
I get that the sum of the exterior angles of a convex polygon add up to 360 degrees but I have a feeling the way Sal explained it in the video is more on the intuitive side. It is not a demonstration of sorts. Is this concept maybe one of those "intuitively obvious" things that cannot really be proved but is taken as given nonetheless?
Well the way Sal explained it does not provide a proof for all convex polygons, or 'the general case'. He just made this to show us the intuitive way of finding the sum of the exterior angles.
However I'm pretty sure there is a way to prove this, though I haven't seen the proof myself. Good question though.
However I'm pretty sure there is a way to prove this, though I haven't seen the proof myself. Good question though.
Yup, haven't seen a "mathematically rigorous" proof either, that's why I was asking. Wasn't sure there is one. :) But I'm guessing I'll find it in some video somewhere as I progress further.
Thanks for the answer!
Thanks for the answer!
How do you find out the measure of the interior angles with only information about the measure of exterior angles?
Exterior angles and interior angles are supplementary. Thus
Interior Angle = π  exterior angle (in radians)
Interior Angle = 180°  exterior angle (in degrees)
Interior Angle = π  exterior angle (in radians)
Interior Angle = 180°  exterior angle (in degrees)
Do any of your teachers make you do two column proofs like a chart that seperates and says statement and reason because mine does and its really annoying
I agree that the proofs can be annoying, but I think they are about the most valuable skills that you can learn in geometry. No, you will most likely not need to be able to prove which triangles in a complex drawing are congruent. However, the skill of being able to think your way through a problem, systematically, stepbystep, logically, without making unwarranted assumptions, is a very valuable skill.
So, I'd agree it is annoying at first, but it is a skill worth knowing.
So, I'd agree it is annoying at first, but it is a skill worth knowing.
Yes, when I was in High School we had to do it too. And I agree they are very annoying, but they do lead to a better understanding of geometry.
then how do you find the interior angles of a convex polygon?
http://www.khanacademy.org/math/geometry/polygonsquadsparallelograms/v/sumofinterioranglesofapolygo this is the video. hope that helps! :)
Watch the video "Sum of the interior angles of a polygon".
we all know that!
To find out only one exterior angle(of a convex polygon), do you do 360/ number of sides?
No you do not.
For anyone who is confused. Basically what Sal was trying to say was that every Convex polygon has all of its angles adding up to 360 degrees.
Sal is *not* saying "that every Convex polygon has all of it angles adding up to 360 degrees." He is saying that the sum of all the *exterior* angles of a convex polygon is 360 degrees. The sum of the interior angles depends on the number of the sides of the polygon. The concept of the sum of the interior angles of a polygon is covered in other videos.
So for every polygon, even if it had 800 sides, would the exterior angles always add up to 360, assuming it is a convex polygon?
Also, what about a concave polygon? Does the part that is caved inwards have an external angle, although it is over 180 degrees? Or is it just the other exterior angles that are not caved in that add up to 360 degrees?
Also, what about a concave polygon? Does the part that is caved inwards have an external angle, although it is over 180 degrees? Or is it just the other exterior angles that are not caved in that add up to 360 degrees?
What is the sum of the exterior angles of a concave polygon?
I am slow at math, so bear with me if I get confused but I understand this video in bits and pieces. How do they decide where to draw the lines out to determine the exterior angle of the polygon? Why did he make corresponding angles with parallel lines (transversals) if we're not deducing each angle measurement and only finding out that because of some drawing it will always equal 360 for any convex polygon? Seems a little too indepth if the explanation is really that simple. If it is always 360 degrees, why do we need to know the drawing and adjacent angle explanations? That just threw me off. Can anyone explain that part as well? Thanks in advance.
So confusing not helpful
Are concave polygons also add up to 360 degrees?
no, the external angles of a concave polygon do not add up to 180... for example, take a 6 sided concave polygon with one internal reflex angle.. the sum of the external angles in this case turns out to be 540=180*5+360*1(4*180) where the (4*180) is sum of internal angles!
explain how you can determine if a polygon is concave
If you can draw diagonals outside a shape, then that shape is a concave polygon.
I do not know what ur talking about, but I know that a property of a parralelagram is that the diagonals congruently bisect each other.
I am just curious, but what happens when you have a concave polygon?
The sum is still 360 but you have to subtract the negative angles caused by the concave parts. It is a bit trickier.
is A+B+C+D+E+G+H+I= 360 or is it something else?
The sum of the exterior angles of a polygon with vertices at A,B,C,D,E,F,G,H,I would be 360 degrees. This is a property of the sum of the exterior angles of a polygon.
is there a difference between the sum of the interior angles of a square and a trapezoid and for all quadrilaterals
No any quad that isn't concave (dented) would make 2 triangles so it would be 180 * 2 or 360 interior.
How do you find the exterior angles of a conCAVE polgon, then?
What previous video is he referencing in the beginning?
Sum of Interior Angles of a Polygon ?
Of course he's not talking about exterior because we are watching that right now.
He's talking about Quadrilateral Overview.
He's talking about exterior angles, not interior angles.
In astronomy, what causes  in the case of regular convex polygons ("regular" convex structures)  the sum of the interior angles to be infinite and the sum of the exterior ones to be constant?!
a Platonic solid is a regular, convex polyhedron with congruent faces of regular polygons and the same number of faces meeting at each vertex. Five solids meet those criteria, and each is named after its number of faces.
Why is is that the sum of the exterior angles for all polygons is 360 degrees no matter haw many sides the polygon has?
Because all a polygon is is a circle with sides. We define a circle as not having any sides, and having its points all equally distanced away from one point. We've given circles 360 degrees to better explain them, and as a result, any closed figures' exterior angles must add to 360.
what if there is more than six angles?
When adding up the exterior angles of convex polygons, it doesn't matter how many angles there are. The sum of them is ALWAYS 360 degrees. I'm sorry, I cannot watch the video, because it isn't working for me right now. But by the title I think Mr. Khan was proving this for all polygons. For all convex polygons, the sum of the exterior angles is always 360 degrees.
At 3:29, doesnt convex have a second meaning?
Could you find that concave angle by making it into a triangle?
how do you determine how to solve a regular polygon equation
what do you mean by solving to find a regular polygon equation?
convex means what exactly?
What is a convex region
I have a question please answer...does this rule of 360 degrees apply to all polygons?
Yes. It does. Now when you start thinking about regular polygons, really cool patterns start to show up.
wouldn't an un closed polygon have an exterior angle something different than 360
a "unclosed polygon" doesn't exsist
A polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. Therefore, there is no such thing as an unclosed polygon.
Is the sum of exterior angles 360 for all polygons? And how about triangles?
Triangles also have exterior angles of 360 for the sums. An equalateral triangle has 60˚ for each _interior_ angle. That means that each exterior angle _must_ be 120˚. 120*3 is 360. Hope this helped you understand better!
How do you find the perimeter of Convex and Concave polygons?
what is a convex polygon
?
?
Here's a nonrigorous definition: If you can *always* draw a line from any point in the polygon to any other point in the polygon without going outside the polygon, it is convex.
More at Wikipedia: http://en.wikipedia.org/wiki/Convex_polygon
More at Wikipedia: http://en.wikipedia.org/wiki/Convex_polygon
A polygon in which all the interior angles are less than 180 degrees.
does a concave polygon also have a measure of 60 degrees?
How do you know when you're supposed to add the interior, or the exterior angles. That's the only reason I can't pass this part. Please help!
So are all exteriors just 360 and then you divide the shape for interiors with triangles?
what is the exact equation for exterior angles
add all the measures of the exterior angles and set them equal to 360
At 1:39,shouldn`t angle A be + to point B?
Is this true for all polygons that the exterior angles are equal to 360?
Yes. All exterior angles add up to 360.
The sum of the exterior angles of any convex polygon is 360°
at 1:14 how am i supposed to copy the angle without a protractor? and if i had a protractor, i could easily use it to find the angles without doing this
wait so why cant it work for concave polygons ?
This might be a stupid question but how can it equal 360 degrees? a perfect circle is 360 degrees so that would make every polygon a broken circle, but you cant square a circle? So if you have say a square that exterior angles = 360 degrees wouldnt it be able to have the same area as a circle?
Anything that goes around that doesn't have a beginning or end = 360 degrees.
No because it has those extra areas outside the circle. This is a really great question though.
how do i algabraically make a hexagon add up to 360?
Is there a better way to find out if a polygon is a convex polygon? If we don't know the angles in degrees, we can't be sure that it really does equal 360 degrees, can we? I think I'm confused, haha.
In the video, Sal also did not know about the measurement of any triangle, but he was able to prove it anyways.
What about the formula: (n2) x 180?
It is used to find sum of the interior angles. N = number of sides.
When you know the number of triangles formed,how do you find the sum of the interior angles of a polygon
You multiply the number of triangles by 180 and that's the sum of the interior angles.
I'm still confused as to how to find the sum of all interior angles. Can somebody please explain it in an easier way?
Are all exterior polygons 360 degrees?
Yes, the sum of the exterior angles for ANY polygon is 360, making the very interesting formula:
```S(Exterior Angles) = 360 degrees```
```S(Exterior Angles) = 360 degrees```
What makes a polygon convex?
in the video the captions are in Chinese ....what do I do?
wait, so is every polygon's exterior angle is 360 degrees?
it's applicable only for CONVEX...don't forget that part!
Yes. If the polygon is regular you can also take out the sum of the angles using this property.
but what if it is a regular polygon? do you just do the same thing, knowing that exterior angles are the same as the interior angle or is there an another way to find out.
how did mathmatishins crieit degreases
p.s sorry for my spelling
p.s sorry for my spelling
at 4:46 you just said it's true about convex polygans,what about cancave polygans?
I just think that it's true about concave polygans too,isn't it?
I just think that it's true about concave polygans too,isn't it?
If the sum of interios angles of any polygon is (s2)*180, then sum of all exterior angles must be 360.Considering that number of exterior angles equal the number of vertices of the polygon, then the sum of exterior angles must be equal to [[180*number of Vertices]  [s2]*180 (i.e.the sum of the interior angles)].Why does this not work for concave polygons?
For the concave vertex there isn't an exterior angle in the traditional sense as it's going to be greater than 180 degrees. If you did try and calculate one anyway, you would have a negative angle, at which point the angles would still sum to 360.
This is a good site to see how it works. http://www.mathopenref.com/polygonexteriorangles.html
This is a good site to see how it works. http://www.mathopenref.com/polygonexteriorangles.html
What is the difference between concave and convex polygons? (P.s.: did I use the right terms?)
Concave polygons are polygons that "cave in". If you extend all the sides forever, at least two lines will go through the polygon. Convex polygons are polygons which don't "cave in". If you extend all the sides forever, none of the sides must go through the polygon.
Hope this helps! (P.s: You did!)
Hope this helps! (P.s: You did!)
Why doesnt it work for a convave polygon?
does this apply to all polygons
If they are convex, yes
what is the sum of interior convex angles?
For all polygons would the sum of the exterior angles be 360 degrees or would it be 90 degrees for each exterior angle?
The exterior angles of any polygon equals 360 degrees.
can you make a video with how to find the measure of the sides of the parallelograms and rhombus and how to find the angles using their properties
is the polygon , means more than one sides , am a little confused??
def Polygon: A closed plane figure bounded by three or more line segments. It comes from the Greek polygonos which means 'manyangled'. So any 2dimensional object with three or more sides is a polygon (triangles, rectangles, octagons etc).
How would you work out the exterior or interior angle of a concave polygon?
so how would you find the measure of the exterior angle
take the interior angle next to and subtract it from 180 or take the 2 opposite interior angle from the exterior angle and add them up
I'm still terribly confused as to when to use the triangle concept and when to use the circle concept. Sometimes it's hard to tell the difference between concave and convex polygons because the concave polygons are not always "caved" in.
Polygons are composed of straight sides. A circle does not have straight sides, it has curving sides
Can a polygon have a higher angle than 360?
so a concave polygon has one angle greater than 180 degrees?
If any of the angles on the interior of the polygon are acute, it is concave
Is it also 360 degrees for a triangle?
Yes, and for any convex polygon.
Is geometry part of algebra?
Some parts of geometry are a part of algebra, but fir the most part, geometry is geometry. You do use a lot of algebra in geometry in solving segments, tangents and equal angles. So, in a way, algebra s the language of geometry.
Is there some similar rule for finding sum of exterior angles of concave shapes?
if the measure of an exterior angle of a regular polygon is 45 degrees then the polygon is A. a decagon
B.a an octagon
C.a pentagon
D.a square
B.a an octagon
C.a pentagon
D.a square
The polygon exterior angles theorem says that the sum of the measures of the exterior angles of a convex polygon one angle at each vertex is 360. What does one angle at each vertex mean?
vertex are points, make those points into angles
how to you find the exterior angles of a concave polygon ?
Actually, it's the same as a convex polygon. The sum is also 360°
a regular polygon has 20 degrees, find the number of sides it has
I am assuming that the sum of interior angles is 20 degrees.
lets take the number of sides as n
(n2) * 180 = 20 degrees (sum of interior angles of a polygon having n sides is (n2) * 180)
180*n  360 = 20
n = 19/2
which is not possible so that means it is not a polygon instead for having a polygon the sum of interior angles must be equal or more than 180 degrees.
lets take the number of sides as n
(n2) * 180 = 20 degrees (sum of interior angles of a polygon having n sides is (n2) * 180)
180*n  360 = 20
n = 19/2
which is not possible so that means it is not a polygon instead for having a polygon the sum of interior angles must be equal or more than 180 degrees.
im trying to find the values of the variables for the polygon, triangle.
What is the major difference between Convex and Concave Polygon?
A convex polygon can never have an interior angle that is greater than 180 degrees. A concave polygon can. That's the major difference. I hope this helps!
Why don't this method work for Concave Polygon and why it only works for Convex Polygon? What is the reason behind it?
Why is there no sound in this video!
your computer is probably messed up
At 4:35, Sal explains a way that he remembers concave and convex... Is there any other way?
In Spanish _con_ means _with_ so concave can mean _with cave_. Another trick to determining concavity is to imagine an elastic band being stretched around the figure, does it touch all sides or does it have to span a gap. If it has to span a gap then the figure must be concave (having a cavity or cave).
Concave can be remembered as the angle 'caving' in.
The sum of the exterior angles of a polygon, including a regular, is 360 degrees, right? Or is it just for convex polygons?
What is the difference between a convex and concave polygon?
A convex polygon is any polygon with vertices (corners) pointing outwards. The concave polygon is the opposite. Concave polygons have angles pointing inwards, so it's kind of "caved" in.
What exactly is a CONVEX polygon?
Convex polygons Jadi Josh are polygons which are sort of puffed out, they have no indentations or negative angles.
Hope this helps!
Hope this helps!
Its the opposite of a CONCAVE polygon
How do you know when to use this strategy and when to use the 180(s2) strategy from the sum of interior angles of a polygon video?
I think you can use that strategy all the time with the interior angles of any kind of polygon
example: triangle is 180(3sides 2)
square is 180(42)
example: triangle is 180(3sides 2)
square is 180(42)
When I click on these links, it sends me to YouTube. Then, it says I haven't seen the video and I get no credit for it. It used to work before, but not anymore so how do I fix it?
Could you demonstrate that a regular convex polygon with infinite sides has a total sum of exterior angles that is infinite?
Watch the video ; it will help a lot.
Thank you :)
Watch the video ; it will help a lot.
Thank you :)
Man, I'm learning this stuff in Honors Geometry right now.
Where is the video that sal referenced at 0:00
Does this apply to concave polygons ?
No it does not. The rule that all the exterior angles of a polygon add up to 360 only works on convex polygons.
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