Question

Find the sum of the measures of the interior angles of a regular 30-gon. Then find the measure of eachinterior angle and each exterior angle.The sum of the measures of the interior angles is1. The measure of each interior angleand themeasure of each exterior angle is

Answer 1

Given data:

The given 30-gons.

Thee measurement of interior angle of 30-gons is,

`\begin{gathered} S=(30-2)180^(\circ) \\ =5040^(\circ) \end{gathered}`

The measurement of each interior angle is,

`\begin{gathered} a=(5040^(\circ))/(30) \\ =168^(\circ) \end{gathered}`

The measurement of each exterior angle is,

`\begin{gathered} e=(360^(\circ))/(30) \\ =12^(\circ) \end{gathered}`

Thus, the sum of all exterior angle is 5040°, measurement of each interior angle is 168°, and measurement of each exterior angle is 12°.