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.