Question

what is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72°

Answer 1

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

$Exterior=\frac{360}{n}$

It is given that the measure of each exterior angle of a regular polygon is 72°.

$72=\frac{360}{n}$

Multiply both sides by n.

$72n=360$

Divide both sides by 72.

$n=\frac{360}{72}$

$n=5$

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

$Sum=(n-2)\times 180$

Substitute n=5.

$Sum=(5-2)\times 180$

$Sum=3\times 180$

$Sum=540$

Therefore the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72° is 540°.

Answer 2

Answer:

108°

Step-by-step explanation: