Question

how many sides would a regular polygon have if each interior angle measures 176°?
____sides

Explanation:

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

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

Step2: Substitute the given value of the interior angle into the formula

We are given that \(\theta = 176^{\circ}\), so we have the equation \(176=\frac{(n - 2)\times180}{n}\)

Step3: Cross - multiply

\(176n=(n - 2)\times180\)

Step4: Expand the right - hand side

\(176n = 180n-360\)

Step5: Move the terms with \(n\) to one side

\(180n-176n = 360\)

Step6: Simplify

\(4n=360\)

Step7: Solve for \(n\)

\(n=\frac{360}{4}=90\)

Answer:

\(90\)