Practicing Success
In the given figure, AP is perpendicular to BC, and AQ is the bisector of angle PAC. What will be the measure of angle PQA? |
50° 60° 30° 75° |
60° |
We know that, In ΔAPC, AP ⊥ BC = ∠APC = 90° ∠ACP = 30° = ∠PAC = 180° - (∠APC + ∠ACP) = ∠PAC = 180° - (90° + 30°) = 60° We also know that, AQ is the angle bisector of ∠PAC =∠PAQ = ∠CAQ = ∠PAQ = 60°/2 = 30° Now, ∠PAQ + ∠APC + ∠PQA = 180 = 30 + 90 + ∠PQA = 180 ∠PQA = 180 - 120 = 60o |