Question

what is the measure of an exterior angle of a regular 13 - sided polygon? enter your answer as a decimal in the box. round to the nearest tenth of a degree.

Explanation:

Step1: Recall the formula for exterior angles of a regular polygon

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular \(n\)-sided polygon, the measure of each exterior angle \(E=\frac{360^{\circ}}{n}\).

Step2: Substitute \(n = 13\) into the formula

When \(n = 13\), we have \(E=\frac{360}{13}\).

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Step3: Round to the nearest tenth

Rounding \(27.6923\cdots\) to the nearest tenth. The digit in the hundredth place is \(9\), so we round up the digit in the tenth place. \(27.6923\cdots\approx27.7\)

Answer:

\(27.7\)