Question

what is the measure of an exterior angle of a regular 11 - 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 the measure of an exterior angle of a regular polygon

The sum of the exterior angles of any polygon is $360^{\circ}$. 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 $n = 11$ into the formula

Here, $n = 11$. So, $\theta=\frac{360}{11}$.

Step3: Calculate the value

Using a calculator, $\frac{360}{11}\approx32.727$.

Step4: Round to the nearest tenth

Rounding $32.727$ to the nearest tenth, we look at the hundredths place. Since $2\lt5$, we get $32.7$.

Answer:

$32.7$