Question

In Figure, if AB || CD || EF, PQ || RS, angle RQD = 25° and angle CQP = 60°, then Zangle QRS = ?​

Answer 1

Answer:

145°

Step-by-step explanation:

AB || CD || EF (Given)

PQ || RS  (Given)

∠ RQD = 25° (Given)

∠ CQP = 60° (Given)

According to the figure -

∠ DQR = ∠ QRA = 25° ( Alternate interior angles)

∠ PQC = ∠ BRS = 60°  ( Alternate exterior angles)

∠ QRA + ∠ ARS = ∠QRS  

= ∠QRA + (180° – ∠BRS) [ Linear pair axioms]

= 25° + 180° - 60°

= 205° - 60°

= 145°

Therefore, the value of ∠QRS is 145°.

Answer 2

Answer:

Step-by-step explanation:

(i) AB || CD || EF (Given)

PQ || RS  (Given)

∠ RQD = 25° (Given)

∠ CQP = 60° (Given)

According to the figure -

∠ DQR = ∠ QRA = 25° ( Alternate interior angles)

∠ PQC = ∠ BRS = 60°  ( Alternate exterior angles)

∠ QRA + ∠ ARS = ∠QRS  

                           = ∠QRA + (180° – ∠BRS) [ Linear pair axioms]

                           = 25° + 180° - 60°

                           = 205° - 60°

                           = 145°

Therefore, the value of ∠QRS is 145°.

(ii) ∠PQC + ∠PQD = 180° ( Linear pair axioms )

   60° + ∠PQD = 180°

   ∠PQD = 180° - 60°

   ∠PQD = 120°

∠PQD + ∠RQD = ∠RQP

∠RQP = 120° + 25°  

∠RQP = 145°