Question

an interior angle of a regular convex polygon is 140°. how many sides does the polygon have?

a. 8
b. 9
c. 10
d. 11

Explanation:

Step1: Find the measure of an exterior angle

The sum of an interior angle and its corresponding exterior angle of a polygon is \(180^{\circ}\).
If the interior angle is \(140^{\circ}\), then the exterior angle \(e = 180^{\circ}- 140^{\circ}=40^{\circ}\)

Step2: Use the formula for the number of sides of a regular polygon

The sum of all exterior angles of any polygon is \(360^{\circ}\). For a regular polygon with \(n\) sides, \(n=\frac{360^{\circ}}{e}\) (where \(e\) is the measure of one exterior angle)
Substitute \(e = 40^{\circ}\) into the formula: \(n=\frac{360^{\circ}}{40^{\circ}} = 9\)

Answer:

B. 9