Question

How many degrees are there in the each interior angle of a polygon, if the sum of its interior angles is 2520°?

Answer 1

To find the measure of each interior angle of a polygon, you can use the formula: (n-2) * 180, where n is the number of sides. So, in this case, we have (n-2) * 180 = 2520. The measure of each interior angle of the polygon is 180 degrees.

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=2520 \end{cases}\implies 2520=180(n-2) \\\\\\ \cfrac{2520}{180}=n-2\implies 14=n-2\implies 16=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=16 \end{cases}\implies 16\theta =180(16-2) \\\\\\ 16\theta =2520\implies \theta =\cfrac{2520}{16}\implies \boxed{\theta =157.5^o}`