Question

find the measure of each interior angle and each exterior angle of a regular pentagon (a five - sided polygon).
measure of each interior angle =
measure of each exterior angle =

Explanation:

Step1: Find interior angle

For a regular polygon with \( n \) sides, the formula for the measure of each interior angle is \( \frac{(n - 2)\times180^{\circ}}{n} \). A pentagon has \( n = 5 \). Substitute \( n = 5 \): \( \frac{(5 - 2)\times180^{\circ}}{5}=\frac{3\times180^{\circ}}{5}=\frac{540^{\circ}}{5} = 108^{\circ} \).

Step2: Find exterior angle

The sum of exterior angles of any polygon is \( 360^{\circ} \). For a regular polygon, each exterior angle is \( \frac{360^{\circ}}{n} \). For \( n = 5 \): \( \frac{360^{\circ}}{5}=72^{\circ} \). Also, interior and exterior angles are supplementary, so \( 180^{\circ}- 108^{\circ}=72^{\circ} \), which confirms it.

Answer:

Measure of each interior angle = \( 108^{\circ} \)
Measure of each exterior angle = \( 72^{\circ} \)