What type of polygon must have angles that each measure 108?
Assuming that you mean the inside angle is 108 the answer is a
pentagon.
Each angle inside the polygon forms an acute angle on the
outside with the next side. The measurement of the exterior acute
angle is:
180 - 108 = 72 .
Since all the acute angle around the outside must add up to 360
we find:
360 / 72 = 5
There are five acute angles and therefore five sides to the
polygon.