Math / Geometry

Question13. Find the measure of an exterior angle of a regular pentagon.

Studdy Solution

STEP 1

1. A regular pentagon has all sides and angles equal.
2. The sum of the exterior angles of any polygon is $360^\circ$ .

STEP 2

1. Understand the properties of a regular pentagon.
2. Calculate the measure of one exterior angle.

STEP 3

A regular pentagon is a five-sided polygon where all sides and angles are equal. Each exterior angle is formed by extending one side of the pentagon. The sum of all exterior angles in any polygon is always $360^\circ$ .

STEP 4

To find the measure of one exterior angle of a regular pentagon, we divide the total sum of the exterior angles by the number of sides (or angles) in the pentagon. Since the sum of the exterior angles is $360^\circ$ and there are 5 sides, we have:
$\text{Measure of one exterior angle} = \frac{360^\circ}{5}$

STEP 5

Perform the division:
$\frac{360^\circ}{5} = 72^\circ$
The measure of an exterior angle of a regular pentagon is:
$\boxed{72^\circ}$

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