Question

solve the following please.

Answer 1

∠QPS = ∠RPS

In ΔPQT

∠PQT + ∠PTQ + ∠QTP = 180°

∠PQT + 90° + ∠QTP = 180°

∠PQT = 90 - ∠QPT   ...................(1)

In Δ PTR

∠PRT + ∠TPR + ∠PTR = 180°

∠PRT + ∠TPR + 90° = 180°

∠PRT = 90 - ∠TPR   ....................(2)

1 & 2 subtract

∠Q - ∠R =  (90° - ∠QTP) - (90° - ∠TPR)

∠Q - R = ∠TPR - ∠QTP

∠Q - ∠R = (∠TPS + ∠RPS) - (∠QPS - ∠TRS)

∠Q - ∠R = ∠TPS + ∠RPS - QPS + ∠TRS

∠Q - ∠R = 2∠TPS                           (∠RPS = QPS SO CANCELLED)

∴ ∠TPS = 1/2 (∠Q - ∠R)