Question

the ratio between exterior angle and interior angle of the regular polygon is 1 ratio 5 find the number of sides of the polygon

Answer 1

Let us assume that 1a is the exterior angle and 5a is the interior angle.
Therefore, 1a + 5a = 180
Therefore, 6a = 180
Therefore, a = 180/6 = 30

Therefore, measure of interior angle = 5a = 5 x 30* = 150*
Therefore, measure of exterior angle = 1a = 1 x 30* = 30*
Exterior Angle has a measure of 360/n degrees
The measure of each interior angle is 150*
Since, the measure of the ext. angle is 30* (for each angle)
Therefore, the sides = 360/30 = 12 sides - to calculate sides (360/n) where "n" represents the measure of the exterior angle