Question

Determine the measure of each angle of a regular pentagon, regular nonagon.

Answer 1

Regular pentagon

$$\alpha=\dfrac{360\degree}{5}=72\degree$$

$$\beta=\dfrac{180\degree(5-2)}{5}=108\degree$$

$$interior\ angle=108\degree$$

The interior and exterior angle add up to 180°

$$exterior\ angle=180\degree-\beta=180\degree-108\degree$$

$$exterior\ angle=72\degree$$

Regular nonagon

$$\alpha=\dfrac{360\degree}{9}=40\degree$$

$$\beta=\dfrac{180\degree(9-2)}{9}=140\degree$$

$$interior\ angle=140\degree$$

The interior and exterior angle add up to 180°

$$exterior\ angle=180\degree-\beta=180\degree-140\degree$$

$$exterior\ angle=40\degree$$