Quantitative Aptitude Ques 1469

Question: ABCD is a cyclic quadrilateral and AD is a diameter. If $ \angle DAC=55{}^\circ , $ then the value of $ \angle ABC $ is

Options:

A) $ 55{}^\circ $

B) $ 35{}^\circ $

C) $ 145{}^\circ $

D) $ 125{}^\circ $

Show Answer

Answer:

Correct Answer: C

Solution:

  • In $ \Delta ACD, $ $ \angle DAC=55{}^\circ $ [given] $ \angle ACD=90{}^\circ = $ Angle in a semi-circle
    $ \angle ADC=180{}^\circ -90{}^\circ -55{}^\circ $ $ =180{}^\circ -145{}^\circ =35{}^\circ $ Now, in a cyclic quadrilateral sum of opposite angles $ =180{}^\circ $ $ \angle ABC+\angle ADC=180{}^\circ $ $ \angle ABC=180{}^\circ -\angle ADC=180{}^\circ -35{}^\circ =145{}^\circ $
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