Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3 : 4. Find the sum of the number of sides of each polygon.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 15.
Given:
S1/S2 = 1/2 and Q1/Q2 = 3/4
Now,
Q1/Q2 = 3/4
⇒ (180 - 360/S1)/(180 - 360/S2) = 3/4
⇒ (1 - 2/S1)/(1 - 2/S2) = 3/4
⇒ 4 - 8/S1 = 3 - 6/S2
⇒ 1 = 8/S1 - 6/S2
⇒ 1 = 8/S1 - 6/2S1 [Since S2 = 2S1]
⇒ S1 = 5
And
S2 = 2S1 = 10
Required sum = S1 + S2 = 5 + 10 = 15