Question

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

Explanation:

Step1: Find exterior angle measure

The interior and exterior angles of a polygon are supplementary, so:
$180^\circ - 140^\circ = 40^\circ$

Step2: Relate exterior angle to sides

For any convex polygon, the sum of exterior angles is $360^\circ$. For a regular polygon with $n$ sides, each exterior angle is $\frac{360^\circ}{n}$. Set equal to $40^\circ$:
$$n = \frac{360^\circ}{40^\circ}$$

Step3: Calculate number of sides

Simplify the division:
$n = 9$

Answer:

B. 9