In Δ PQR, ∠Q > ∠R, PS is the bisector of ∠P and PT is perpendicular to PQ. If ∠SPT = 28° and ∠R = 23°, then the measure of ∠Q is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 33°
∠SPT = 28°
∠PRS = 23°
Now, as PT is perpendicular to QP:
∠QPT = 90° = ∠SPT + ∠QPS
⇒ 90° = 28° + ∠QPS
⇒ ∠QPS = 62°
Now,
∠QPS = ∠P/2
So, ∠P = 62° × 2 = 124°
Hence,
∠Q = 180° - (124° + 23°) [Angle sum property]
⇒ ∠Q = 33°