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Q148 (IAS/2001) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Quantitative aptitude topics Answer Verified

In the figure below, ABCD is a cyclic quadrilateral, AB = BC and angle BAC = 70°, then angle ADC is

Result
Your answer: —  ·  Correct: D
Explanation

AB = BC makes triangle ABC isosceles with B as the apex, so the base angles at A and C are equal; hence ∠CAB (given as ∠BAC) = ∠BCA = 70°. Therefore ∠ABC = 180° − 70° − 70° = 40°. For a cyclic quadrilateral opposite angles are supplementary, so ∠ADC + ∠ABC = 180°. Thus ∠ADC = 180° − 40° = 140°. Therefore the correct choice is option 4 (140°).

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