You’re given that the polygon has two pairs of complementary interior angles. Since each pair of complementary angles adds up to 90 degrees, the sum of these two pairs would be 90 * 2 = 180 degrees.
Your also given that the polygon has three sets of supplementary interior angles. Since each set of supplementary angles adds up to 180 degrees, the sum of these three sets would be 180 * 3 = 540 degrees.
Now, find the sum of all the interior angles of the polygon. The sum of all interior angles of an n-sided polygon can be found using the formula (n-2) * 180 degrees.
So, in this case, the sum of all the interior angles of the polygon is (n-2) * 180 degrees.
Your given that the sum of the remaining interior angles is 1440 degrees. So, you can set up the equation:
(n-2) * 180 - (180 + 540) = 1440
Simplifying the equation:
(n-2) * 180 - 720 = 1440
(n-2) * 180 = 2160
Dividing both sides by 180:
n-2 = 12
Adding 2 to both sides:
n = 14
So that means the polygon has 14 sides.
