In ∆ABC, the perpendiculars drawn from A, B and C meet the opposite sides at points D, E and F, respectively,. AD, BE and CF intersect at point P. If ∠EPD = 110° and the bisectors of ∠A and ∠B meet at point Q, then ∠AQB = ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 125°
∠EPD = 1100
In ΔABC if the angle bisector of ∠B and ∠C meet at a point O inside the triangle then -
∠BOC = 900 + ∠A/2
In the diagram -
DPEC is quadrilateral.
∠C = 3600 - (∠P + ∠D + ∠E)
∠C = 3600 - (1100 + 900 + 900)
∠C = 3600 - 2900 = 700
According to the concept -
∠AQB = 900 + 70/2 = 900 + 350 = 1250