The size of each interior angle of a regular polygon is 11 times the size of each exterior angle. Work out how many sides the polygon has.

The way to tackle this particular question requires the need for 2 formula equationsThe sum of all the interior angles of a regular polygon can be worked out by subtracting 2 from the number of sides, and multiplying this by 180 as this creates triangles within the polygon (Would show with diagram). We can then divide this by the number of sides to work out each individual angle.The sum of all the exterior angles of a regular polygon is 360 degrees. Therefore each individual exterior angle is worked out by dividing 360 by the number of sides. The question states that the interior angle is 11*the exterior and hence we can equate these equations like so:(n-2)180 / n = 11 (360/n)We can therefore simplify this. by multiplying both by n to get:(n-2)180 = 11360 Dividing by 180 gets us:n-2 = 22Therefore n (the number of sides) is 24