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
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.
To find the number of sides of a polygon given the sum of its interior angle measures, we can use the formula S = 180(n – 2), where S is the sum of the angle measures and n is the number of sides.
In this case, we are given that S = 1260 degrees. We can substitute this value into the formula and solve for n:
1260 = 180(n - 2)
Dividing both sides by 180:
7 = n - 2
Adding 2 to both sides:
n = 9
So, the polygon has 9 sides.
To find the number of sides in the polygon, we can use the formula for the sum of the interior angles of a polygon.
The formula is S = 180(n - 2), where S is the sum of the interior angles and n is the number of sides.
Given that the sum of the interior angles is 1,260 degrees, we can substitute this value into the formula:
1,260 = 180(n - 2)
Now, let's solve for n:
Divide both sides by 180:
1,260 / 180 = n - 2
7 = n - 2
Add 2 to both sides:
7 + 2 = n - 2 + 2
9 = n
Therefore, the polygon has 9 sides.