Question

question 14 of 27
which of the following best describes a regular polygon when the sum of its interior angles is 1260°?

a. hexagon
b. octagon
c. nonagon
d. pentagon

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \), where \( S \) is the sum of the interior angles and \( n \) is the number of sides.

Step2: Substitute the given sum into the formula and solve for \( n \)

We know that \( S = 1260^{\circ} \). Substitute this into the formula:
\[

$$\begin{align*} 1260&=(n - 2)\times180\\ \frac{1260}{180}&=n - 2\\ 7&=n - 2\\ n&=7 + 2\\ n&=9 \end{align*}$$

\]
A polygon with 9 sides is called a nonagon.

Answer:

C. Nonagon