Question

D is a point on the side BC of △ABC. A line PDQ through D, meets side AC at P and AB produced at Q If ∠A=80°, ∠ABC=60° and ∠PDC=15°, find a) ∠AQD b) ∠APD.

Answer 1

∠ABD and ∠QBD form a linear pair.

∠ABC + ∠QBC =180°

60° + ∠QBC = 180°

∠QBC = 120°

∠PDC = ∠BDQ (Vertically opposite angles)

∠BDQ = 75°

In ∆QBD:

∠QBD + ∠QDB + ∠BDQ = 180° (Sum of angles of ∆QBD)

120°+ 15° + ∠BQD = 180°

∠BQD = 180°– 135°

∠BQD = 45°

In ∆AQP:

∠QAP + ∠AQP + ∠APQ = 180° (Sum of angles of ∆AQP)

80° + 45° + ∠APQ = 180°

∠APQ = 55°

∠APD = ∠APQ

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Answer 2

Answer:

Step-by-step explanation:

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