Question

the degree measure of each interior angle in a regular polygon can be expressed as $m=\frac{180(n - 2)}{n}$, where $n$ is the number of sides in the polygon. which shows the equation solved for the number of sides, $n$? $n=\frac{m + 180}{2}$ $n=\frac{360}{2 - m}$ $n=\frac{180(m + 2)}{m}$ $n=\frac{360}{180 - m}$ $n = 180(m - 2)$ $n=\frac{180}{m + 2}$

Explanation:

Step1: Start with given formula

$m=\frac{180(n - 2)}{n}$

Step2: Cross - multiply

$mn=180(n - 2)$

Step3: Expand the right side

$mn = 180n-360$

Step4: Move terms with $n$ to one side

$mn-180n=-360$

Step5: Factor out $n$

$n(m - 180)=-360$

Step6: Solve for $n$

$n=\frac{360}{180 - m}$

Answer:

$n=\frac{360}{180 - m}$