Question

how many sides would a convex polygon have if each interior angle measures 172°?
45
39
58
35
none of these answers are correct.

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 \(172^{\circ}\), then the exterior angle \(e = 180^{\circ}- 172^{\circ}=8^{\circ}\)

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

The sum of the exterior angles of any convex 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 \(e = 8^{\circ}\) into the formula: \(n=\frac{360^{\circ}}{8^{\circ}} = 45\)

Answer:

A. 45