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.
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.
Let's assume the number of sides of the polygon is n.
We know that the sum of the interior angles of a polygon can be found using the formula (n-2) * 180°, where n is the number of sides.
Since each interior angle is 128°, the sum of all the interior angles can also be calculated by multiplying 128° by the number of sides:
128° * n
Now, we can set up an equation based on the information given:
(n-2) * 180° = 128° * n
Let's solve this equation for n:
180°n - 360° = 128°n
Combine like terms:
52°n = 360°
Divide both sides by 52°:
n = 360°/52°
Simplifying:
n ≈ 6.923
Since the number of sides of a polygon must be a whole number, we can conclude that the polygon has 7 sides.