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SSC CGL 2021 PYQ — Question 51

SSC CGL - 17 Aug 2021 - Shift 2 • Quantitative Aptitude • Q51

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ABCD is a cyclic quadrilateral such that AB is the diameter of the circle and ∠ADC = 145°, then what is the measure of ∠BAC?

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Correct answer: C

Explanation

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

As one knows that the sum of the opposite angle in a cyclic quadrilateral is 180°.

So ∠\angleABC = 180 - 145 = 35°

One also knows that the sum of the angle in a semicircle is 90°.

So ∠\angleACB = 90°.

The sum of the interior angle of a triangle is 180°.

∠BAC = 180 - 90 - 35 = 55°