what is the sum of the measures of the interior angles of the stop sign?
if the stop sign is a regular octagon, what is the measure of each
interior angle?

Question

Accepted Answer

# Explanation:
## Step1: Find the sum of interior angles
The formula for the sum of interior angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For an octagon, $n = 8$.
$$
\begin{align*}
S&=(8 - 2)\times180^{\circ}\
&=6\times180^{\circ}\
&=1080^{\circ}
\end{align*}
$$
## Step2: Find the measure of each interior angle
If the octagon is regular, then each interior angle $\theta=\frac{(n - 2)\times180^{\circ}}{n}$. Substitute $n = 8$ into the formula.
$$
\begin{align*}
\theta&=\frac{(8 - 2)\times180^{\circ}}{8}\
&=\frac{6\times180^{\circ}}{8}\
&=\frac{1080^{\circ}}{8}\
& = 135^{\circ}
\end{align*}
$$

# Answer:
The sum of the measures of the interior angles of the stop sign (octagon) is $1080^{\circ}$. The measure of each interior angle of a regular octagon is $135^{\circ}$.

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QUESTION IMAGE

Question

Explanation:

Step1: Find the sum of interior angles

Step2: Find the measure of each interior angle

Answer: