Each exterior angle of a regular polygon measures 60. What is the sum of the interior angles?

Question

need it be the shortest but not the direct method 

 

Answer 1

The sum of the exterior angles of a regular polygon is 360º.

Each exterior angle of a regular polygon is 360º/n

360º/n=60º

360/60=n

6=n

A polygon with 6 sides is a hexagon.

Use the formula (n-2)*180

(6-2)*180=4*180=720º

another solution...

you have 6 interior angles (hexagon)

if an exterior angle is 60º, the corresponding interior angle is 180-60=120º

you have 6 of these 120º angles

6*120=720º again