Question

the measure of an exterior angle of a regular polygon is $45^{circ}$. find the number of sides of the polygon.

Explanation:

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

The sum of the exterior angles of any regular polygon is \( 360^\circ \). For a regular polygon, each exterior angle \( \theta \) is equal, and the number of sides \( n \) is given by the formula \( n=\frac{360^\circ}{\theta} \), where \( \theta \) is the measure of one exterior angle.

Step2: Substitute the given exterior angle measure into the formula

We are given that \( \theta = 45^\circ \). Substituting this into the formula \( n=\frac{360^\circ}{45^\circ} \).

Step3: Calculate the number of sides

\( \frac{360^\circ}{45^\circ}=8 \).

Answer:

The number of sides of the regular polygon is 8.