Question

The sum of interior angles of two regular polygons of sides n and n+2 are in the ratio 3:4.Calculate the sum of the interior angles of the polygon with a n sides.

A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees

Answer 1

To find the sum of the interior angles of a polygon, use the formula (n-2) * 180, where n is the number of sides. The sum of the interior angles of a polygon with n sides can be calculated as (540n - 1080)/4.

Step-by-step explanation:

To find the sum of the interior angles of a polygon, we use the formula (n-2) * 180, where n is the number of sides of the polygon. Let's assume the polygon with n sides has a sum of interior angles x.

According to the given information, the polygon with (n+2) sides has a sum of interior angles 4x/3. We can set up the equation (n-2) * 180 = 4x/3 and solve for x.

1. Multiply both sides of the equation by 3 to eliminate the fraction: 3 * [(n-2) * 180] = 4x
2. Distribute 3 to simplify: 540n - 1080 = 4x
3. Divide both sides of the equation by 4: x = (540n - 1080)/4

Therefore, the sum of the interior angles of the polygon with n sides is (540n - 1080)/4. To calculate the specific value, substitute the given number of sides into the formula.