Question

Find the measures of an interior and an exterior angle of a regular pentagon

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

• Measure of interior angle.

,

• Measure of exterior angle.

Given:

Number of sides of the polygon = 5

Step 1

Find the sum of the interior angle of the polygon using the formula below:

`\begin{gathered} sum\text{ of interior of n-sided=\lparen n-2\rparen180} \\ \\ =(5-2)180 \\ \\ =3*180 \\ \\ =540\degree \end{gathered}`

Step 2

Determine the measure of each of the interior angles.

`\begin{gathered} measure\text{ of interior angle=}(540)/(5) \\ \\ =108\degree \end{gathered}`

Step 3

Find the measure of the exterior angle using the formula below:

`\begin{gathered} exterior\text{ angle=}(360)/(n) \\ \\ =(360)/(5) \\ \\ =72\degree \end{gathered}`

ANSWER

• measure of an interior angle =108°

• measure of an exterior angle = 72°