Question

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what is the measure of an exterior angle in a regular polygon with 13 sides? write your answer as an integer or as a decimal rounded to the nearest tenth. submit

Explanation:

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

The sum of the exterior angles of any regular polygon is \( 360^\circ \). For a regular polygon with \( n \) sides, each exterior angle \( \theta \) is given by the formula \( \theta=\frac{360^\circ}{n} \).

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

Here, \( n = 13 \), so we calculate \( \theta=\frac{360}{13} \).

Step3: Perform the division

\( \frac{360}{13}\approx27.6923 \), and when rounded to the nearest tenth, we get \( 27.7 \).

Answer:

\( 27.7 \)