Question

What is the measure of each interior angle does a polygon have if the sum of its interior angles is 1800°?

Answer 1

150

Explanation:

Answer 2

`\underset{in~degrees}{\textit{Sum of All Interior Angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ S=1800 \end{cases}\implies 1800=180(n-2)\implies \cfrac{1800}{180}=n-2 \\\\\\ 10=n-2\implies 12=n \\\\[-0.35em] ~\dotfill`

`\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=12 \end{cases}\implies 12\theta =180(12-2) \\\\\\ 12\theta =1800\implies \theta =\cfrac{1800}{12}\implies \boxed{\theta =150^o}`