Question

The ratio between the exterior and interior angle of a regular polygon is 1:5, find

a. the measure of each exterior angle.
b. the measure of each interior angle.
c. the number of sides of the polygon.

Answer 1

Exterior and interior angles are supplementary, meaning they sum to 180 degrees. If the exterior and interior angles are x and 5x respectively, we can write x + 5x = 180, and solving for x we get x = 30°. This means that the answer to a) is 30° and the answer to b) is 30 * 5 = 150°.

For c), to find the number of sides we can do:

180 - 150 = 30

180 / 30 = 6 so the answer to c) is 6.