Question

The interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. The sum S of the measures of the interior angles of a polygon with n sides can be found using the formula S = 180(n – 2). The sum of a polygon’s interior angle measures 1,260 degrees. How many sides does the polygon have? (1 point) Responses 3 3 5 5 7 7 9 9

Answer 1

To find the number of sides of a polygon with a sum of interior angle measures of 1,260 degrees, we can use the formula S = 180(n – 2), where S is the sum of the interior angles and n is the number of sides.

Let's substitute the given value:
1,260 = 180(n – 2)

Next, we solve the equation for n:

Divide both sides by 180:
1,260 / 180 = n – 2

Simplify:
7 = n – 2

Add 2 to both sides:
7 + 2 = n – 2 + 2

Simplify:
9 = n

Therefore, the polygon has 9 sides.