The sum of interior angels and the sum of exterior angles of polygon are in the ratio 9:2.find the sides of regular polygon.
The sum of the exterior angles of any polygon is 360°
the interior sum is 180(n-2), where n is the number of sides
so 180(n-2) = 360
n-2 = 2
n = 4
so it is true for any quadrilateral
To find the number of sides of a regular polygon, we need to know that the sum of the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon.
Let's assume the number of sides of the regular polygon is n. Therefore, the sum of the interior angles is (n-2) * 180 degrees.
Now, let's calculate the sum of the exterior angles of the polygon. The sum of the exterior angles of any polygon is always 360 degrees.
Given that the ratio of the sum of the interior angles to the sum of the exterior angles is 9:2:
((n-2) * 180) / 360 = 9/2
To solve this equation, let's cross-multiply:
2 * ((n-2) * 180) = 360 * 9
Simplifying the equation:
(n-2) * 180 = 360 * 9 / 2
(n-2) * 180 = 180 * 9
Dividing both sides by 180:
n-2 = 9
Adding 2 to both sides:
n = 9 + 2
Therefore, the number of sides of the regular polygon is:
n = 11
Thus, the regular polygon has 11 sides.