Question

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Answer 1

Answer:

x = 120°

y = 77°

Step-by-step explanation:

AB || CD [Given]

Here, PQ and PR are the transversals.

∴ ∠APQ = ∠PQR [Interior Alternate Angles]

∴ ∠PQR = 60°

∠PQR + x = 180° [Sum of Adjacent Angles = 180°]

  60°   +  x = 180°

∴ x = 180° - 60°

  x = 120°

Now,

∠BPR + ∠PRD = 180° [Sum of cointerior angles = 180°]

∠BPR + 137° = 180°

∴ ∠BPR = 180° - 137°

             = 43°

Now,

∠APQ + ∠QPR + ∠BPR = 180° [Sum of all angles on a straight line =

                                                 180°]

60° + y + 43° = 180°

y + 103° = 180°

∴ y = 180° - 103°

  y = 77°