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 \(360^\circ\). If each exterior angle of a regular polygon is \(x\) and the number of sides is \(n\), then \(n\times x = 360^\circ\).

Step2: Substitute the given exterior angle measure

We are given that \(x = 45^\circ\). Substituting into the formula \(n=\frac{360^\circ}{x}\), we get \(n=\frac{360^\circ}{45^\circ}\).

Step3: Calculate the number of sides

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

Answer:

The number of sides of the polygon is 8.