Question

6. Find the measure of oneinterior angle of a regular 30-gon.

Answer 1

The sum of the interior angles of a polygon is given by:

$\text{Sum}=(n-2)\times180$

Where n is the number of sides of the polygon.

A regular 30-gon has 30 sides, then the sum is:

$\begin{gathered} \text{Sum}=(30-2)\times180 \\ \text{Sum}=28\times180 \\ \text{Sum}=5040 \end{gathered}$

Now, we have to divide the total sum by the number of angles, then:

$\frac{5040}{30}=168$

Answer: One interior angle of a regular 30-gon measures 168°.