Madhya Pradesh Police Exam Model Paper 6

GIVEN:
PQ || RS, ∠QPT = 120° and ∠PTR = 15°
CALCULATION:
Considering the given figure
Extend line SR that cuts PT at L,Since, PQ || RS PQ || SL is also true.
So,
$\angle \mathit{Q}\mathit{P}\mathit{L}+\angle \mathit{P}\mathit{L}\mathit{R}=180°$
$\angle \mathit{P}\mathit{L}\mathit{R}=180-\angle \mathit{Q}\mathit{P}\mathit{L}$
$\Rightarrow \angle \mathit{P}\mathit{L}\mathit{R}=180°\mathit{–}120°=60°$
Now,
∠PLR = ∠LRT + ∠LTR (External angle theorem)
$\Rightarrow \angle \mathit{L}\mathit{R}\mathit{T}=60°\mathit{–}15°=45°$
Now,
$\angle \mathit{S}\mathit{R}\mathit{T}+\angle \mathit{L}\mathit{R}\mathit{T}=180°$
$\therefore \angle \mathit{S}\mathit{R}\mathit{T}=180°\mathit{–}45°=135°$