Question

how many sides does a regular polygon have if each interior angle measures 168°?

Explanation:

Step1: Find the measure of each exterior angle

The sum of an interior angle and its corresponding exterior angle of a polygon is \(180^{\circ}\).
If the interior angle is \(168^{\circ}\), then the exterior angle \(e = 180^{\circ}-168^{\circ}=12^{\circ}\)

Step2: Use the formula for the measure of an exterior angle of a regular polygon

The formula for the measure of an exterior angle \(e\) of a regular polygon with \(n\) sides is \(e=\frac{360^{\circ}}{n}\)
We know \(e = 12^{\circ}\), so \(n=\frac{360^{\circ}}{e}\)
Substitute \(e = 12^{\circ}\) into the formula: \(n=\frac{360^{\circ}}{12^{\circ}} = 30\)

Answer:

The regular polygon has \(30\) sides.