Question

1. a stop sign is a regular octagon with eight congruent sides and eight congruent angles. what is the sum of the measures of the interior angles?

a. 780°
b. 1260°
c. 900°
d. 1080°

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 \( S=(n - 2)\times180^{\circ} \).

Step2: Identify the number of sides of the octagon

A stop sign is a regular octagon, so the number of sides \( n = 8 \).

Step3: Substitute \( n = 8 \) into the formula

Substitute \( n = 8 \) into \( S=(n - 2)\times180^{\circ} \), we get \( S=(8 - 2)\times180^{\circ} \).
First, calculate \( 8-2 = 6 \).
Then, calculate \( 6\times180^{\circ}=1080^{\circ} \).

Answer:

D. \( 1080^{\circ} \)