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 ?

147°

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 \({147}^\circ\)