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 the sum of interior angles

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a pentagon, \(n = 5\). So, \((5 - 2)\times180^{\circ}=3\times180^{\circ} = 540^{\circ}\).

Step2: Find each interior angle

Since a regular pentagon has all interior angles equal, each interior angle is \(\frac{540^{\circ}}{5}=108^{\circ}\).

Step3: Find each exterior angle

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular pentagon, each exterior angle is \(\frac{360^{\circ}}{5} = 72^{\circ}\).

Answer:

Measure of each interior angle = \(108\)°
Measure of each exterior angle = \(72\)°