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:
[tex]\begin{gathered} sum\text{ of interior of n-sided=\lparen n-2\rparen180} \\ \\ =(5-2)180 \\ \\ =3\times180 \\ \\ =540\degree \end{gathered}[/tex]
Step 2
Determine the measure of each of the interior angles.
[tex]\begin{gathered} measure\text{ of interior angle=}\frac{540}{5} \\ \\ =108\degree \end{gathered}[/tex]
Step 3
Find the measure of the exterior angle using the formula below:
[tex]\begin{gathered} exterior\text{ angle=}\frac{360}{n} \\ \\ =\frac{360}{5} \\ \\ =72\degree \end{gathered}[/tex]
ANSWER
• measure of an interior angle =108°
• measure of an exterior angle = 72°
