In the regular nonagon shown, what is the measure of angle x?

Solution:

We know that

Sum of interior angles of a polygon = (n - 2) 180°

Where n is the number of sides

From the question, for a nonagon n = 9

Sum of interior angles of a nonagon = (9 - 2)180° = 1260°

In a regular nonagon, each interior angle has same degree = 1260/9 = 140°

In the figure,

x is the exterior angle

Exterior angle = 180° - Interior angle

Exterior angle = 180° - 140° = 40°

Therefore, the measure of angle x is 40°.

In the regular nonagon shown, what is the measure of angle x? 

Summary:

In the regular nonagon shown, the measure of angle x is 40°.