In triangle ABC, the perpendiculars 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 = 116° and the bisectors of ∠ A and ∠ B meet at Q. Then the measure of ∠ AQB is ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 122°.
∠ EPD = 116° [Given]
From the figure:
∠C = 360 - [116 + 90 + 90] = 64°
Now,
Q is the Incenter of the triangle.
So,
∠AQB = 90° + (∠C/2)
∠ AQB = 90° + 32° = 122°