Question

Find the number of sides of a polygon if the sum of the measures of its interior angles is four times the sum of the measures of its exterior angles?

Answer 1

Answer: 10 sides

Step-by-step explanation:

Any polygon has its exterior angles add to 360 degrees. Four times this is 4*360 = 1440 which is the sum of the interior angles of this particular polygon.

S = sum of the interior angles

S = 180(n-2)

1440 = 180(n-2)

n-2 = 1440/180

n-2 = 8

n = 8+2

n = 10

There are 10 sides to this polygon. It is a decagon.