In the diagram, QP//ST:PQR = 34∘ ∘ QRS = 73∘ ∘ and RS = RT. Find SRT

In the diagram, QP//ST:PQR = 34${}^{\circ }$ QRS = 73${}^{\circ }$ and RS = RT. Find SRT

Answer Details

Construction joins R to P such that SRP = straight line

R = 180${}^{\circ }$ - 107${}^{\circ }$

< p = 180${}^{\circ }$ - (107${}^{\circ }$ - 34${}^{\circ }$)

108 - 141${}^{\circ }$ = 39${}^{\circ }$

Angle < S = 39${}^{\circ }$ (corr. Ang.) But in $△$SRT

< S = < T = 39${}^{\circ }$

SRT = 180 - (39${}^{\circ }$ + 39${}^{\circ }$)

= 180${}^{\circ }$ - 78${}^{\circ }$

= 102${}^{\circ }$