SSC CGL 2021 PYQ — Question 58

SSC CGL - 18 Aug 2021 - Shift 3 • Quantitative Aptitude • Q58

ABCD is a cyclic quadrilateral AB and DC meet at F, when produced. AD and BC meet at E, when produced. If $\angle$ BAD = 68º and $\angle$ AEB = 27º, then what is the measure of $\angle$ BFC?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 17º.

From the above figure,

$\angle$ FBC = 68 + 27 (Exterior angle is equal to the sum of opposite interior angle).

$\angle$ FBC = 95°

$\angle$ FCB = $\angle$ DAB = 68° (Alternate segment theorem)

$\angle$ BFC = 180 - 95 -68 = 17°