In ΔABC, ∠A = 66°, BD ⊥ AC and CE ⊥ AB. BD and EC intersect at P. The bisectors ∠PBC and ∠PCB meet at Q. What is the measure of ∠BQC ?
Answer & explanation
Correct answer: option 4
In the quadrilateral AEPD
∠EAD + ∠PEA + ∠EPD + ∠PDA = \({360}^\circ\)
⇒ ∠EPD = \({360}^\circ\) - (\({66}^\circ\) + \({90}^\circ\) + \({90}^\circ\))
⇒ ∠EPD = \({114}^\circ\)
From figure
∠EPD = \({114}^\circ\) = ∠BPC
∠BQC = \({90}^\circ\) + \(\frac{∠BPC}{2}\)
∠BQC = \({90}^\circ\) + \(\frac{114}{2}\) = \({90}^\circ\) + \({57}^\circ\) = \({147}^\circ\) (since ∠EPD and ∠BPC are vertically opposite angles ).
Therefore, ∠BQC is \({147}^\circ\)