Question

The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?

Answer 1

The sum of exterior angles of any polygon is 360 degrees.

The sum of interior angles of any polygon is given by 180(n-2) degrees, n = number of sides.

So the sum of the measure of interior angles, or 180(n-2) is equal to 5 times the sum of the measure of exterior angles, or 360.

180(n-2) = 5*360

Can you solve for n?

Answer 2

i got n=12. is this correct?

Answer 3

it is :)