Question

the measure of an exterior angle of a regular polygon is given below. find the measure of an interior angle. then find the number of sides.
20
what is the measure of an interior angle?
160
how many sides does the polygon have?

Explanation:

Step1: Find interior angle measure

For a regular polygon, exterior angle (\(e\)) and interior angle (\(i\)) are supplementary, so \(i = 180^\circ - e\). Given \(e = 20^\circ\), then \(i = 180^\circ - 20^\circ = 160^\circ\).

Step2: Find number of sides

The sum of exterior angles of any polygon is \(360^\circ\). Let \(n\) be the number of sides. Then \(n=\frac{360^\circ}{e}\). Substituting \(e = 20^\circ\), we get \(n=\frac{360^\circ}{20^\circ}=18\).

Answer:

• Measure of interior angle: \(160^\circ\)
• Number of sides: \(18\)