Question

An exterior angle of a regular polygon measures 45 degrees. What is the measure of an interior angle?

135 degrees
145 degrees
45 degrees

Answer 1

The exterior angle of a polygon and its corresponding interior angle always add up to 180°.

Let the interior angle of the polygon be $y^{\circ}$

$45^{\circ}+y=180^{\circ}$

So, $y=180^{\circ}-45^{\circ}$

$y=135^{\circ}$

So, the interior angle of the polygon is $135^{\circ}$