Question

find the measure of one interior angle in the regular polygon. the measure of each interior angle is \\(\square^{\circ}\\). (type an integer.)

Explanation:

Step1: Identify the polygon type

The figure is a regular pentagon, so the number of sides \( n = 5 \).

Step2: Use the interior angle formula

The formula for the sum of interior angles of a polygon is \( S=(n - 2)\times180^\circ \). For \( n = 5 \), \( S=(5 - 2)\times180^\circ=3\times180^\circ = 540^\circ \).

Step3: Find one interior angle

In a regular polygon, all interior angles are equal. So one interior angle \(=\frac{S}{n}=\frac{540^\circ}{5}=108^\circ \).

Answer:

\( 108 \)