PQR is a non-isosceles right-angled triangle, right angled at Q

In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT= PT, then what is ∠RLM equal to?

  1. ∠PQT
  2. ∠LRM
  3. ∠RML
  4. ∠QPT

Answer

Since QT = PT, ∠QPT = ∠PQT

Since LM and QT are parallel, ∠RLM = ∠LQT

Also, in right-angled triangle PQR, ∠LRM = 90° - ∠QPT

∠LRM = 90° - ∠PQT = ∠LQT = ∠RLM

The correct option is B.