Question

what is the measure of an exterior angle in a regular polygon with 19 sides? write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

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

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

Step2: Substitute \(n = 19\) into the formula

We have \(n = 19\), so we substitute this value into the formula \(\theta=\frac{360^\circ}{n}\).
\(\theta=\frac{360^\circ}{19}\approx18.947^\circ\)

Step3: Round to the nearest tenth

Rounding \(18.947^\circ\) to the nearest tenth, we look at the hundredth place. The digit in the hundredth place is \(4\), which is less than \(5\), so we round down. So \(\theta\approx18.9^\circ\)

Answer:

\(18.9\)