Question

how many sides does a regular polygon have if each interior angle measures 168°?

Explanation:

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

The formula for each interior angle \(\theta\) of a regular polygon with \(n\) sides is \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\). We know that \(\theta = 168^{\circ}\), so we set up the equation \(\frac{(n - 2)\times180}{n}=168\).

Step2: Solve the equation for \(n\)

First, multiply both sides of the equation by \(n\) to get rid of the denominator: \((n - 2)\times180=168n\).
Expand the left - hand side: \(180n-360 = 168n\).
Subtract \(168n\) from both sides: \(180n-168n-360=0\), which simplifies to \(12n-360 = 0\).
Add 360 to both sides: \(12n=360\).
Divide both sides by 12: \(n=\frac{360}{12}=30\).

Answer:

The regular polygon has 30 sides.