UPSC Prelims 2001 · General Studies

Question 148: Basic Numeracy

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

a40°

b80°

c110°

d140°

AnswerThe answer is (d).

In triangle ABC, AB = BC, so the angles opposite them are equal: angle BCA = angle BAC = 70 degrees. So angle ABC = 180 - 70 - 70 = 40 degrees. In a cyclic quadrilateral opposite angles add up to 180 degrees, so angle ADC = 180 - angle ABC = 140 degrees.

Why each option is right or wrong

(a) 40 degrees is angle ABC, not angle ADC.
(b) 80 degrees does not follow from the angles.
(c) 110 degrees does not follow from the angles.
(d) Right: 140 degrees.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2001, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.