Question

if each interior angle of a regular polygon measures 108°, how many sides does the polygon have? the polygon has \\(\square\\) sides.

Explanation:

Step1: Find exterior angle measure

The interior and exterior angles of a polygon are supplementary, so:
$180^\circ - 108^\circ = 72^\circ$

Step2: Use total exterior angle sum

The sum of exterior angles of any polygon is $360^\circ$. Let $n$ = number of sides:
$n = \frac{360^\circ}{72^\circ}$

Step3: Calculate number of sides

$n = 5$

Answer:

5