Question

using the polygon interior angle sum theorem
an interior angle of a regular polygon has a measure of 120°, what type of polygon is it?
decagon hexagon quadrilateral
octagon

Explanation:

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

The formula for the measure of an interior angle \(\theta\) of a regular polygon with \(n\) sides is \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\)

Step2: Substitute \(\theta = 120^{\circ}\) into the formula

We have \(120^{\circ}=\frac{(n - 2)\times180^{\circ}}{n}\)

Step3: Solve the equation for \(n\)

Multiply both sides by \(n\): \(120n=(n - 2)\times180\)
Expand the right - hand side: \(120n = 180n-360\)
Subtract \(120n\) from both sides: \(0=180n - 120n-360\)
Simplify: \(0 = 60n-360\)
Add \(360\) to both sides: \(60n=360\)
Divide both sides by \(60\): \(n = 6\)

Answer:

hexagon