Question

question 11 how many sides would a regular polygon have if each interior angle measures 171°? sides

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 \(\theta = 171^{\circ}\) into the formula

We have \(171=\frac{(n - 2)\times180}{n}\)

Step3: Cross - multiply

\(171n=(n - 2)\times180\)

Step4: Expand the right - hand side

\(171n = 180n-360\)

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

\(180n-171n = 360\)

Step6: Simplify

\(9n=360\)

Step7: Solve for \(n\)

\(n = 40\)

Answer:

\(40\)