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: Determine the number of sides (n)

The polygon shown is a pentagon, so \( n = 5 \).

Step2: Use the formula for the sum of interior angles

The formula for the sum of the interior angles of a polygon is \( S=(n - 2)\times180^{\circ} \).
Substitute \( n = 5 \) into the formula:
\( S=(5 - 2)\times180^{\circ} \)
\( S = 3\times180^{\circ} \)
\( S = 540^{\circ} \)

Step3: Find the measure of one interior angle

In a regular polygon, all interior angles are equal. So, to find the measure of one interior angle, divide the sum of the interior angles by the number of sides (\( n \)):
\( \text{Measure of one interior angle}=\frac{S}{n} \)
Substitute \( S = 540^{\circ} \) and \( n = 5 \):
\( \text{Measure of one interior angle}=\frac{540^{\circ}}{5} \)
\( \text{Measure of one interior angle}=108^{\circ} \)

Answer:

\( 108 \)