Question

1. how many sides does an equiangular polygon have if each interior angle measures 156°? (h)

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 \(156^{\circ}\), then the exterior angle \(e = 180^{\circ}- 156^{\circ}=24^{\circ}\)

Step2: Use the formula for the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\).
Let \(n\) be the number of sides of the polygon. We know that \(n=\frac{360^{\circ}}{e}\) (where \(e\) is the measure of one exterior angle)
Substitute \(e = 24^{\circ}\) into the formula: \(n=\frac{360^{\circ}}{24^{\circ}} = 15\)

Answer:

The equiangular polygon has \(15\) sides.