The sum of interior angles of an irregular polygon is 5040 .find the number of sides of the polygon
Since the angles of an n-gon sum to 180(n-2)
you have
180(n-2) = 5040
n-2 = 28
n = 30
To find the number of sides of an irregular polygon, we can use the formula for the sum of the interior angles of a polygon.
The formula for the sum of the interior angles of a polygon is given by:
Sum = (n - 2) * 180
Where n is the number of sides of the polygon.
In this case, we are given that the sum of the interior angles is 5040. So we can set up the equation:
5040 = (n - 2) * 180
To solve for n, we can rearrange the equation to isolate n:
(n - 2) * 180 = 5040
Divide both sides of the equation by 180:
n - 2 = 5040 / 180
Simplify the right side:
n - 2 = 28
Add 2 to both sides:
n = 28 + 2
n = 30
Therefore, the number of sides of the polygon is 30.
To find the number of sides of an irregular polygon, you can utilize the formula:
Sum of interior angles = (n - 2) * 180
Where n is the number of sides of the polygon.
In this case, the sum of interior angles is given as 5040, so we can set up the equation:
5040 = (n - 2) * 180
To solve for n, divide both sides of the equation by 180:
5040 / 180 = n - 2
Simplifying the left side:
28 = n - 2
Finally, add 2 to both sides of the equation:
28 + 2 = n
Therefore, the number of sides of the polygon is 30.