There's a 15 sided regular polygon. I need to find the angle of the triangle formed by joining one corner of the polygon and it's alternate vertex.

Question

8th grade maths...

Answer 1

There are (15-2)*180 = 2340 degrees in the regular 15-gon

 

2340/15 = 156 degrees in each of the corner pockets.

 

Connecting the lines from the vertices to the center creates

15 triangles, and they are all congruent by SSS.

 

So that leaves 78 degree base angles for each triangle, which 

makes the angle from the center opposite the base 180 - 78 - 78 = 24.