Question

find the measures of an interior angle and an exterior angle of a regular pentagon. the measure of an interior angle is \boxed{}

Explanation:

Step1: Calculate sum of interior angles

For an \(n\)-sided polygon, sum of interior angles is \((n-2) \times 180^\circ\). For pentagon, \(n=5\):
$$(5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$$

Step2: Find one interior angle

Divide total by number of angles (\(n=5\)):
$$\frac{540^\circ}{5} = 108^\circ$$

Step3: Find exterior angle

Interior + exterior angle = \(180^\circ\):
$$180^\circ - 108^\circ = 72^\circ$$

Answer:

The measure of an interior angle is \(108^\circ\), and the measure of an exterior angle is \(72^\circ\)