Question

The sum of the measure of the interior angles of a polygon is 1080°.

What polygon is it?

hexagon
triangle
decagon
octagon

Answer 1

Basically test each polygon (except for the triangle). We know triangle definitely isn't it:

Test Hexagon
360/6 = 60 (exterior angle)
180 - 60 = 120 (interior angle)
120*6 = 720 (Sum of interior)

Test Decagon:
360/10 = 36 (exterior angle)
180 - 36 = 144 (interior angle)
144 x 10 = 1440 (Sum of Interior)

Test Octagon:
360/8 = 45 (exterior angle)
180 - 45 = 135 (interior angle)
135*8 = 1080 (Sum of Interior)

Therefore, the polygon with a sum of interior angles of 1080 degrees is an octagon.