Question

Find the number of sides a regular polygon must have to meet each condition.

Each interior angle measure equals each exterior angle measure.

Each exterior angle measure is one eighth the measure of each interior angle.

Answer 1

Exterior angle of a regular n-sided polygon = 360°/n

Interior angle = 180° - 360°/n

So, with 360/n = (1/8)(180 - 360/n)

360/n = 180/8 - 360/(8n)

(360/n)*(9/8) = 180/8

2*9/n = 1

n = 18