Question

4) In the given figure, AB||CD, √APQ=45° and √BPR= 75°, Find all the angles of ∆PQR​

Answer 1

Answer:

angle PQR = 45°

angle PRQ = 75°

angle QPR = 60°

Step-by-step explanation:

AB || CD [Given]

angle APQ = 45°

angle BPR = 75°

angle APQ = angle PQR [Alternate angles]

angle BPR = angle PRQ [Alternate Angles]

In triangle PQR,

angle PQR = 45° [Proved above]

angle PRQ = 75° [Proved above]

angle PQR + angle PRQ + angle QPR = 180° [Sum of all interior angles of a  triangle equals 180°]

45° + 75° + angle QPR = 180°

120° + angle QPR = 180°

∴ angle QPR = 180° - 120°

                     = 60°