In an △ABC, ∠A = 66°, BDꞱ AC, and CE Ʇ AB. BD and EC intersect at P. The bisector ∠PBC and ∠PCB meet at Q.
What is the measure of ∠BQC?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 147°
∠A = 660
The angle formed by the internal bisectors of the angles of the triangle is equal to 90 degrees plus half the third angle.
In Δ ABC -
∠BQC = 90º + ∠BPC/2
In the quadrilateral AEPD -
∠EAP + ∠PEA + ∠EPD + ∠PDA = 3600
∠EPD = 3600 - (660 + 900 + 900)
∠EPD = 1140
From figure -
∠BQC = 90º + ∠BPC/2
∠BQC = 90º + 1140/2 = 1470 (since ∠EPD and ∠BPC are vertically opposite angle).