An interior angle of a regular polygon is 162 degrees,find the sum of it's interior angle?

To find the sum of the interior angles of a regular polygon, we can use the formula:

Sum of interior angles = (n-2) * 180 degrees

where n is the number of sides of the polygon.

Since we know that one interior angle of the regular polygon is 162 degrees, we can find the number of sides by dividing 360 degrees (the sum of the exterior angles of a polygon) by the exterior angle:

Exterior angle = 180 - 162 = 18 degrees

Number of sides = 360 / 18 = 20

Now we can find the sum of the interior angles:

Sum of interior angles = (20-2) * 180 = 18 * 180 = 3240 degrees

Therefore, the sum of the interior angles of the regular polygon is 3240 degrees.

The sum of the interior angles of a regular polygon with n sides is given by the formula:

Sum of interior angles = (n - 2) - 180 degrees

Since each interior angle of the regular polygon is 162 degrees, we can use this formula to find the number of sides n:

162 = (n - 2) - 180

Dividing both sides by 180, we get:

(n - 2) = 0.9

Adding 2 to both sides, we get:

n = 2.9

Since n must be a whole number, the number of sides of the regular polygon is not defined. Therefore, we cannot calculate the sum of its interior angles.