## Polygon Interior Angles
Here's how that's computed: We'll use a pentagon as an example. Start with a pentagon and locate its center: 360 ^{o}/5 = 72^{o}That makes the sum of the other 2 angles of each triangle 180 ^{o} - 72^{o} = 108^{o}.Each of the other angles of the triangle are 108/2 = 54 ^{o} Looking at the image you can see that 2 of these angles makes a pentagon interior angle, so the interior angles of a pentagon are 108 each. ^{o}Let's try this on a larger polygon, one with 20 sides! So, all the triangles vertices meet at the center and there are 20 of them, so each triangle vertex angle = 360 ^{o}/20^{o} = 18^{o}That makes the sum of the other 2 angles 180 ^{o} - 18^{o} = 162^{o} which is the size of the interior angle of a 20-sided figure which, by the way, is an .
icosagon |