Question

What is the measure of the exterior angles of a regular
polygon if the measure of the interior angles is 165°?

A) 25° B) 15° C) 20° D) 10°

Answer 1

We know that the value of an interior angle of a regular 𝑛-sided polygon $=\frac{n-2}{n}\times 180°$
$\Rightarrow 165°=\frac{n-2}{n}\times 180°\Rightarrow 11=\frac{n-2}{n}\times 12\Rightarrow 11n=12n-24\Rightarrow 11n-12n=-24\Rightarrow -n=-24\Rightarrow n=24$


The value of an exterior angle of a regular 𝑛−sided polygon $=\frac{360°}{n}$

The value of an exterior angle of 24-sided polygon $=\frac{360°}{24}=15°$