SOLUTION: if the measure of a vertex angle of a regular polygon is 176, what is the measure of the central angle?

Algebra ->  Polygons -> SOLUTION: if the measure of a vertex angle of a regular polygon is 176, what is the measure of the central angle?       Log On


   

Question 999802: if the measure of a vertex angle of a regular polygon is 176, what is the measure of the central angle?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


A radius of the circumscribed circle to a regular polygon that intersects a vertex of that polygon must bisect the vertex angle. Two such radii that are adjacent form an isosceles triangle with the side of the polygon that joins the two vertices. In this case, the two equal angles of the isosceles triangle each measure one-half of 176, or 88 degrees. Since the sum of the measures of the angles of a triangle is 180 and 180 minus 176 is 4. And the central angle must be 4 degrees.

John

My calculator said it, I believe it, that settles it