CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The ratio of number of sides of two regular polygons are as 5:4 and the difference of there exterior angles is 9o. Find the number of sides of both the polygon.

Open in App
Solution

Let n be the Greatest Common Divisor (GCD) of the numbers under the question.
Then one polygon has 5n sides, while the other has 4n sides.
It is well known fact that the sum of exterior angles of each (convex) polygon is 360o.
So, the exterior angle of the regular 5n-sided polygon is 360o5n.
Similarly, the exterior angle of the regular 4n-sided polygon is 360o4n.
The difference between the corresponding exterior angles is 9o.
360o4n360o5n=9o

14n15n=9o360o

5n4n20n2=140

n20n2=140

1n=12
n=2
Number of sides =4n=2×4=8 and 5n=2×5=10.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Revisiting Geometry
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon