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?
Answer & explanation
Correct answer: option 2
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