One interior angle of a polygon is equal to 80° and each of the interior angles are 128°.Find the number of sides of the polygon.

Answer 1

Let n be the number of sides of the polygon.
The sum of the interior angles of a polygon is given by (n-2) * 180 degrees.
We are given that one interior angle is 80 degrees, so the sum of the remaining (n-1) interior angles is 128 * (n-1) degrees.
Setting up an equation, we have:
(n-2) * 180 = 80 + 128 * (n-1)
Simplifying, we have:
180n - 360 = 80 + 128n - 128
52n = 408
n = 7
Therefore, the polygon has 7 sides.