In ΔPQR, if 4∠P = 5∠Q = 20∠R, then the value of ∠Q is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 72°.
Let 4∠P = 5∠Q = 20∠R = k
So, ∠P = k/4, ∠Q = k/5, and ∠R = k/20
Since the sum of the angles in a triangle is 180°.
∠P + ∠Q + ∠R = 180
⇒ (k/4) + (k/5) + (k/20) = 180
⇒ 10k/20 = 180
⇒ k/2 = 180
⇒ k = 360
⇒ ∠Q = k/5 = 360/5 = 72
Therefore, the value of ∠Q is 72°.