In triangle PQR, PS is the bisector of ∠QPR and PT ⊥ QR with ∠Q > ∠R. What is ∠TPS?
Show answer & explanation
Correct answer: B
Explanation
Given:
In triangle PQR, PS is the bisector of ∠QPR.
PT ⟂ QR
∠Q > ∠R
By formula:
∠QPR = 180° − (∠Q + ∠R)
Since PS is a bisector ⇒ ∠QPS = ∠SPR = (∠QPR)/2
Let ∠Q = Q and ∠R = R.
∠QPR = 180° − (Q + R)
∠QPS = (180° − Q − R) / 2
Since PT ⟂ QR,
It follows that ∠QPT = 90° − Q
∠TPS = ∠QPS − ∠QPT
= (180 − Q − R)/2 − (90 − Q)
= (180 − Q − R − 180 + 2Q)/2
= (Q − R)/2