Question

how many sides does a regular polygon have if the measure of one interior angle is 160°?

Explanation:

Step1: Find the exterior angle measure

The sum of an interior angle and its corresponding exterior angle in a polygon is \(180^\circ\). So, if the interior angle is \(160^\circ\), the exterior angle \(e\) is \(180 - 160 = 20^\circ\).

Step2: Use the formula for the sum of exterior angles

The sum of the exterior angles of any polygon is always \(360^\circ\). For a regular polygon, all exterior angles are equal. Let \(n\) be the number of sides. Then \(n\times e = 360^\circ\). Substituting \(e = 20^\circ\), we get \(n=\frac{360}{20}\).

Step3: Calculate the number of sides

\(n=\frac{360}{20}=18\).

Answer:

The regular polygon has 18 sides.