Question

bonus: if the measure of one interior angle of a regular polygon is 160 degrees, how many sides does the polygon have?

Explanation:

Step1: Recall interior angle formula

For a regular $n$-sided polygon, the measure of one interior angle is $\frac{(n-2)\times180^\circ}{n}$.

Step2: Set up equation with given angle

$$\frac{(n-2)\times180}{n}=160$$

Step3: Solve for $n$

Multiply both sides by $n$: $(n-2)\times180=160n$
Expand left side: $180n-360=160n$
Subtract $160n$: $20n-360=0$
Solve for $n$: $20n=360 \implies n=\frac{360}{20}=18$

Answer:

18