IN ∆PQR, ∠Q =66° and ∠R = 34°. T is a point on QR, and S is a point between Q and T such that PS Ʇ QR and PT is the bisector of ∠QPR. What is the measure of ∠SPT?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 16°
∠QPR = 180 - 66 = 34°
∠QPT = ∠TPR = 40°
In triangle PTR,
∠PTR + ∠PRT + ∠TPR = 180°
∠PTR = 106°
Now,
∠PTS + ∠PTR = 180°
⇒ ∠PTS = 74°
So, ∠SPT = 180 - 90 = 74°
⇒ ∠SPT = 16°