Question

g the polygon interior angle sum theorem
what is the sum of the measures of the interior of the stop sign?
$\boldsymbol{square}^circ$
if the stop sign is a regular octagon, what is the measure of each interior angle?
$\boldsymbol{square}^circ$

Explanation:

Step1: Identify number of sides

A stop sign is an octagon, so $n=8$.

Step2: Calculate interior angle sum

Use the polygon sum formula: $(n-2)\times180^\circ$

$$\begin{align} (8-2)\times180^\circ&=6\times180^\circ\\ &=1080^\circ \end{align}$$

Step3: Find each interior angle (regular)

Divide total sum by number of sides: $\frac{\text{Total Sum}}{n}$

$$\begin{align} \frac{1080^\circ}{8}&=135^\circ \end{align}$$

Answer:

1. $1080$
2. $135$