Number of sides on a polygon

Question

There is a polygon with n sides of equal length. The polygon is partially hidden behind a pentagon with 5 sides showing. Angles A and B are created by the intersection points between the polygon and the pentagon. The sum of angles A and B are equal to 88 degrees. I need to know how to solve for n.

________________

____ / \

/ a / \

/ / \

| / \

| / Pentagon \

| \ /

| \ /

\ b \ /

\____\ /

\ /

\ /

\ /

I know this might not be much but it’s the best that I could do. The angles a and b are made by the pentagon covering all but 5 sides of the shape. If this figure isn’t sufficient, I would have to email or instant message a better one.

Answer 1

Good morning Andrew!

This is a problem with a general solution. They ask for 5 exposed sides of a partially covered regular n-gon implying a hexagon or higher n-gons. From there after setting two equations for the sum of the vertex angles around angle A and angle B each to 360 and solving for n, we get an identity: 360n-720 = 360n-720.

The values of n again will be restricted in the equation to integers 6 and higher to solve it. I hope that helps.