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4) In the given figure, AB||CD, √APQ=45° and √BPR= 75°, Find all the angles of ∆PQR |
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Answer» Answer: angle PQR = 45° angle PRQ = 75° angle QPR = 60° Step-by-step EXPLANATION: 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° |
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