Question

find the measure of each interior angle of a regular pentagon. if needed, round to the nearest tenth.

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon.

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \). For a pentagon, \( n = 5 \).

Step2: Calculate the sum of interior angles of a pentagon.

Substitute \( n = 5 \) into the formula: \( S=(5 - 2)\times180^{\circ}=3\times180^{\circ} = 540^{\circ} \).

Step3: Find the measure of each interior angle of a regular pentagon.

In a regular polygon, all interior angles are equal. So, divide the sum of interior angles by the number of sides (\( n = 5 \)): \( \text{Each interior angle}=\frac{540^{\circ}}{5}=108^{\circ} \).

Answer:

\( 108^{\circ} \)