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# Triangle angle challenge problem

Learn about the sum of exterior angles in a polygon, specifically a pentagon. We find out that the sum of exterior angles is always the same, no matter the shape of the pentagon. To understand this, we use interior angles and divide the pentagon into triangles. Created by Sal Khan.

## Want to join the conversation?

• Why 3 triangles? Why not 4? 5?
• The number of triangles you should use is (number of sides in polygon)-2. So
5-2=3
• Isn't the sum of the exterior angles for ANY regular polygon always going to be 360 degrees? or am I missing something??
• Actually it is true for ALL polygons, not just regular ones.
• video is not full it ends at
• The same thing happened to me, but all you have to do is go to the far right corner of the video and click on the blue words that say something along the lines of "See full video playback." Hope this helps:)
• very confusing, is there any way someone could explain it easier
• Imagine all of the lines that form the exterior angles extending outward to infinity. Now, imagine zooming out from the pentagon, until it shrinks to a point. You'll see all of the lines that we extended just converging to that point. Now, it's clear that all of those angles form a full circle, which is 360°.

Note, you can try this for any polygon.
• isn't the sum of the angles of a pentagon always 540 degrees though??
• Sum of Interior Angles of a Polygon:

``  S(θ) = 180•(n - 2)  : where n = number of sides ``

The sum of exterior angles of any polygon is always `360º`
• Did this video end midway through Sal's commentary for anyone else, or is that just my computer's fault?
• The same thing happened to me, but all you have to do is go to the far right corner of the video and click on the blue words that say something along the lines of "See full video playback." Hope this helps:)
• couldnt you just say that some of the angles were ninety and then get your answer from there?
• No, actually, because this information is never technically given. If any of the angles had that 'square' angle box thingy then you could consider those angles 90 degrees, but it's not mathematically legitimate to assume it. Hope it helps.
• Why don't the exterior angles of a polygon always add up to 180? I thought they did...
• Exterior angles of a polygon always add up to 360 degrees, regardeless of the number of sides. You're thinking of interior angles.
• Ok? that seemed easy but when you try it its really really hard
• It's okay. Start with simpler problems first and then gradually increase the level of difficulty once you are confident about the topic.
• Is there a reason it has to be divided into three triangles? If it was an octagon, for example, (or any other shape) how many triangles would it be divided into?
• An octagon would be divided into six triangles. This is something that is much easier to understand by experimenting than through text, but the number of triangles will always be two less than the number of sides. This is why the formula for interior angles of a polygon is 180(n - 2) where n is the number of sides.