Question

A regular polygon has 20 sides. What is the measure of 1 interior angle

Answer 1

`\bf \textit{sum of interior angles of a polygon}\\\\ n\theta=180(n-2)\qquad \begin{cases} n=\textit{number of sides}\\ \theta=\textit{internal angle}\\ --------------\\ n=20 \end{cases} \\\\\\ thus\implies 20\cdot \theta=180(20-2)\implies 20\cdot \theta=3240 \\\\\\ \theta=\cfrac{3240}{20}`

Answer 2

1 interior angle
= [ ( n-2 ) x 180° ] ÷ 20
=［( 20-2 ) x 180°］÷ 20
= 162°