If the sum of the interior angles of a regular polygon is 1620 degrees. How many sides does the polygon have?
Show work.
The formula for the sum of the interior angles of a regular polygon is (n - 2) * 180, where n is the number of sides.
Therefore, 1620 = (n - 2) * 180
Solving for n, we get:
1620 = (n - 2) * 180
1620/180 = (n - 2)
9 = n - 2
n = 11
Therefore, the polygon has 11 sides.
To find the number of sides in a polygon, we can use the formula for the sum of interior angles of a polygon, which is given by:
Sum = (n - 2) * 180
Here, "Sum" represents the sum of the interior angles, and "n" represents the number of sides in the polygon.
In this case, we are given that the sum of the interior angles is 1620 degrees. So we can set up the equation as:
1620 = (n - 2) * 180
Now, we can solve this equation by rearranging it and solving for "n":
Divide both sides of the equation by 180:
1620 / 180 = n - 2
Simplify the equation:
9 = n - 2
Add 2 to both sides of the equation:
9 + 2 = n - 2 + 2
Simplify further:
11 = n
Therefore, the polygon has 11 sides.
To find the number of sides in a regular polygon, we can use the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n represents the number of sides.
Given that the sum of the interior angles is 1620 degrees, we can set up the equation:
1620 = (n - 2) * 180
Next, we can simplify the equation:
1620 = 180n - 360
Adding 360 to both sides of the equation, we get:
1980 = 180n
Dividing both sides by 180, we find:
n = 1980 / 180
Simplifying the expression on the right side, we get:
n = 11
Therefore, the polygon has 11 sides.