Question

the measure of each interior angle of a regular polygon is 162°. find the number of sides.
number of sides =

Explanation:

Step1: Recall the formula for interior angle of a regular polygon

The formula for the measure of each interior angle \(\theta\) of a regular polygon with \(n\) sides is \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\). We know that \(\theta = 162^{\circ}\), so we set up the equation \(\frac{(n - 2)\times180}{n}=162\).

Step2: Solve the equation for \(n\)

First, multiply both sides of the equation by \(n\) to get rid of the denominator: \((n - 2)\times180=162n\).
Expand the left - hand side: \(180n-360 = 162n\).
Subtract \(162n\) from both sides: \(180n-162n-360=0\), which simplifies to \(18n - 360 = 0\).
Add \(360\) to both sides: \(18n=360\).
Divide both sides by \(18\): \(n=\frac{360}{18}=20\).

Answer:

20