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SSC CGL 2017 PYQ — Question 76

SSC CGL Tier II Quant - 12/01/2017 • Quantitative Aptitude • Q76

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ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, then ∠AED measures:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 55°

Understanding

Application

ABCD is a cyclic quadrilateral of which AB is the diameter.

Diagonals AC and BD intersect at E.

∠DBC = 35°

 

∠ACB = 90° (Angle in semicircle)

In triangle BEC:

∠ECB + ∠EBC + ∠BEC = 180

⇒ ∠BEC = 180 – 90 – 35 = 55°

⇒ ∠BEC = 55°

Now,

∠AED = ∠BEC = 55° [Vertically opposite angles]