Question

6

10. In a regular poligon the interior angle is 11 times the exterior angle.
(i) Work out the number of sides of this polygon




22
(ii) Find the sum of the interior angles of this polygon.
18 0 (0-2)
18ox (22-2)

Answer 1

i. 24 sides

ii. 3960°

Explanation:

Let the exterior angle be x.

x + 11x = 180°

12x = 180°

x = 15°

Hence the size of an interior angle is 11 times 15, which is 165°.

The formula for finding the sum of angles in an interior angle is this:

(n-2)180, with n being the number of sides the polygon has.

Hence, you can form this equation.

(n-2 )180 = 165n

180n-360=165n

-360=-15n

24=n

So, with there being 24 sides, the sum of all interior angles is 24 times 165 which equals 3960°