Answer:
The sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72° is 540°.
Step-by-step explanation:
The formula to find the measure of each exterior angle of a regular polygon is
[tex]Exterior=\frac{360}{n}[/tex]
It is given that the measure of each exterior angle of a regular polygon is 72°.
[tex]72=\frac{360}{n}[/tex]
Multiply both sides by n.
[tex]72n=360[/tex]
Divide both sides by 72.
[tex]n=\frac{360}{72}[/tex]
[tex]n=5[/tex]
It means the number of vertices of the polygon is 5. It means the given polygon is pentagon.
The sum of interior angles of a regular polygon is
[tex]Sum=(n-2)\times 180[/tex]
Substitute n=5.
[tex]Sum=(5-2)\times 180[/tex]
[tex]Sum=3\times 180[/tex]
[tex]Sum=540[/tex]
Therefore the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72° is 540°.
