SSC CGL 2022 PYQ — Question 34

SSC CGL Tier II - Quant - 3 Feb 2022 • Quantitative Aptitude • Q34

In $\Delta$ ABC , $\angle$ A = 50º , BE and CF are perpendiculars on AC and AB at E and F, respectively BE and CF intersect at H. The bisectors of $\angle$ HBC and $\angle$ HCB intersect at P. $\angle$ BPC is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 155º

In Quadrilateral AFHE,

50 + 90 + 90 + $\angle$ FHE = 360

$\angle$ FHE = 180 - 50 = 130°

$\angle$ FHE = $\angle$ BHC = 130° (VOA)

$\angle$ BPC = 90 + 1/2 × 130 = 90 + 65 = 155°.