The number of sides of two regular polygons are in the ratio 4:3. If the difference between their exterior angles is 10°, find the number of sides in each polygon.
Show answer & explanation
Correct answer: C
Explanation
Ratio of the number of sides = 4 : 3
Difference between the exterior angles = 10°
Exterior angle = 360° / n
Let the number of sides be 4x and 3x.
First polygon = 360/(4x)
Second polygon = 360/(3x)
360/(3x) − 360/(4x) = 10
(120/x − 90/x) = 10
30/x = 10
x = 3
Number of sides = 4x = 12 and 3x = 9
12 sides and 9 sides