Question

if an exterior angle of a regular polygon measures 45°, how many sides does the polygon have?
\boxed{} sides

Explanation:

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

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

Step2: Solve for the number of sides \(n\)

We are given that each exterior angle \(\theta = 45^\circ\). Substituting this into the formula \(\theta=\frac{360^\circ}{n}\), we get \(45^\circ=\frac{360^\circ}{n}\). To solve for \(n\), we can rearrange the formula as \(n=\frac{360^\circ}{45^\circ}\).

Step3: Calculate the value of \(n\)

Calculating \(\frac{360}{45}\), we get \(n = 8\).

Answer:

8