Question

Find the measure of each interior angle of the regular polygon.

The measure of each interior angle is _____

Answer 1

well, taking a looksie at the picture above, we can see the polygon has 9 sides, namely a NONAgon, so

`\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=9 \end{cases}\implies 9\theta =180(9-2) \\\\\\ 9\theta =180(7)\implies 9\theta =1260\implies \theta =\cfrac{1260}{9}\implies \theta =140`

Answer 2

interior angle = 140°

Explanation:

the sum of the interior angle of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

here n = 9 , then

sum = 180° × (9 - 2) = 180° × 7 = 1260°

since the polygon is regular then interior angles are congruent, so

measure of each interior angle = 1260° ÷ 9 = 140°