select the correct answer. an interior angle of a regular convex polygon is 140°. how many sides does the…

select the correct answer. 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

select the correct answer. 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

Answer

Explanation:

Step1: Find exterior - angle

The sum of an interior angle and an exterior angle of a polygon is 180°. Given the interior angle is 140°, the exterior angle $\theta=180 - 140=40^{\circ}$.

Step2: Use the formula for the number of sides

The sum of exterior angles of any polygon is 360°. Let the number of sides be $n$. We know that $n=\frac{360}{\text{exterior - angle}}$. Substituting the value of the exterior - angle $\theta = 40^{\circ}$, we get $n=\frac{360}{40}=9$.

Answer:

B. 9