Question

1. one exterior angle of a regular polygon measures 10°, what is the measure of each interior angle? how many sides does the polygon have?

Explanation:

Step1: Find interior angle

Interior and exterior angles of a polygon are supplementary (sum to \(180^\circ\)). So, interior angle \(= 180^\circ - 10^\circ = 170^\circ\).

Step2: Find number of sides

Sum of exterior angles of any polygon is \(360^\circ\). For a regular polygon, each exterior angle is equal. Let \(n\) be the number of sides. Then \(n=\frac{360^\circ}{\text{measure of one exterior angle}}=\frac{360^\circ}{10^\circ} = 36\).

Answer:

Each interior angle measures \(170^\circ\), and the polygon has 36 sides.