Question

please help me to prove

Answer 1

In rt tri PQT
Angle Q = 180 - 90 - angle QPT 1
In rt tri TRP
Angle R = 180 - 90 - angle TPR 2

Subracting 2 from 1
Angle Q - angle R
= 90 - angle QPT - (90 - angle TPR)
= 90- 90- (Angle QPS - Angle TPS) + Angle TPR
= Angle TPS - Angle RPS + Angle RPS+ Angle TPS ( Angle RPS = Angle QPS Given)
= 2 Angle TPS
Angle TPS = 1/2 ( Angle Q - Angle R)
Hence proved
Hope it helps....