Question

how many sides does a regular polygon have if each interior angle measures 162°?

Explanation:

Step1: Find exterior angle measure

The interior and exterior angles of a polygon are supplementary, so:
$180^\circ - 162^\circ = 18^\circ$

Step2: Use total exterior angle sum

The sum of exterior angles of any polygon is $360^\circ$. Let $n$ = number of sides:
$n = \frac{360^\circ}{\text{measure of one exterior angle}}$
$n = \frac{360^\circ}{18^\circ}$

Step3: Calculate number of sides

$n = 20$

Answer:

20