If in triangle PQR, ∠P = 120º, PS is perpendicular to QR at S and PQ + QS = SR, the measure of ∠Q is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 40°
Let the PQ = x & QS = y then SR = PQ + QS = x + y
Take a point T on the SR so that QS = ST = y
TR = SR - ST = x + y - y = x
PT = TR = x [Since QS = ST]
Now,
∠TPR + ∠TRP + ∠PTR = 180
(∠TPR = ∠TRP = x)
⇒ ∠PTR = 180 - 2x
So,
∠PTS = 180 - (180 - 2x) = 2x
∠PTS = ∠PQS = 2x (QP = PT)
Now,
∠PQR + ∠QRP + ∠RPQ = 180
⇒ 2x + x = 180 - 120
⇒ x = 20
Hence,
∠Q = 2x = 40°