Question

find the measure of an exterior angle of a regular decagon.

the measure of an exterior angle of a regular decagon is (square^circ).
(type an integer or a decimal.)

Explanation:

Step1: Recall the formula for exterior angles of a regular polygon

For any regular polygon, the sum of the exterior angles is always \( 360^\circ \). And if the polygon has \( n \) sides, the measure of each exterior angle \( \theta \) is given by the formula \( \theta=\frac{360^\circ}{n} \).

Step2: Determine the number of sides of a decagon

A decagon has \( n = 10 \) sides.

Step3: Calculate the measure of one exterior angle

Substitute \( n = 10 \) into the formula \( \theta=\frac{360^\circ}{n} \). So we have \( \theta=\frac{360^\circ}{10}=36^\circ \).

Answer:

\( 36 \)