Question

Find the measure of each interior angle and each exterior angle of a regular nonagon (a nine-sided polygon).

Measure of each interior angle =
x
5
?
Measure of each exterior angle =

Answer 1

Interior-140° Exterior-40°

Explanation:

The sum of the interior angles of a polygon are given by 180(n-2) where n is the number of sides.

Therefore, the sum of all interior angles in a nonagon is 180(9-2) or 180×7. This equals to 1260°.

To get the individual interior angle, you use
`(s)/(n)`, with n defined above and s being the sum of interior angles.

Therefore, each angle is
`(1260)/(9)`°, which can be solved to 140°.

The value of an individual exterior angle is given by 180-i, with i being the individual interior angle (this is because the 2 angles form a straight line).

In this case, 180-140=40°.

Each interior angle of a nonagon is 140°, and each exterior angle is 40°.

**This content involves angles of polygons, which you may want to revise. I'm always happy to help!