Question

how many sides would a convex polygon have if each interior angle measures 174°?
51
62
77
60
none of these answers are correct.
question 17
1 pts
how many sides would a convex polygon have if each interior angle measures 162°?
29
10
36
16
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 \(162^{\circ}\), then the exterior angle \(e = 180^{\circ}-162^{\circ}=18^{\circ}\)

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 each exterior angle)
Substitute \(e = 18^{\circ}\) into the formula: \(n=\frac{360^{\circ}}{18^{\circ}} = 20\)

Answer:

None of these answers are correct.