The sum of of the interior angles of a polygon is three times it's sum oits exterior angles. How many sides has polygon?

Aliyuus2

1 year ago

The polygon has 8 sides (an octagon) because the sum of its interior angles is three times the sum of its exterior angles.
Here's how to solve it:
Sum of exterior angles: The sum of the exterior angles of any polygon is always 360 degrees.
Sum of interior angles: The sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees.
Set up the equation: We're told the sum of the interior angles is three times the sum of the exterior angles, so: (n-2) * 180 = 3 * 360.
Solve for n:
(n-2) * 180 = 1080
(n-2) = 6
n = 8