In ΔABC, the perpendicular drawn from A, B and C meet the opposite sides at D, E and F respectively. AD, BE and CF intersect at point P. If ∠EPD=114° and the bisectors of ∠A and ∠B meet at Q, then the measure of ∠AQB?
Answer & explanation
Correct answer: option 2
Step 1:
∠EPD = 114°
In Quad. EPDC
∠E = ∠D = 90°
∠C = 180° - 114° = 66°
Step 2:
∠AQB = 90° + \(\frac{∠ACB}{2}\) [Interior angle bisector theorem]
= 90° + \(\frac{66}{2}\) = 123°
⇒∠AQB = 123°