Quantitative Aptitude Ques 2066

Question: The side AC of a $ \Delta ABC $ is extended to D such That $ BC=CD. $ If $ \angle ACB $ is $ 70{}^\circ , $ then $ \angle ADB $ is equal to

Options:

A) $ 35{}^\circ $

B) $ 45{}^\circ $

C) $ 70{}^\circ $

D) $ 110{}^\circ $

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \angle ACB+\angle BCD=180{}^\circ $ [linear pair] $ \angle BCD=180{}^\circ -70{}^\circ =110{}^\circ $ In $ \Delta BCD, $ $ BC=CD $ $ \angle CBD=\angle CDB $ … (i) [angles opposite to equal sides] Also, $ \angle BCD+\angle CBD+\angle CDB=180{}^\circ $ $ 2\angle CDB=180{}^\circ -\angle BCD $ $ =180{}^\circ -110{}^\circ =70{}^\circ $

$ \therefore $ $ \angle CDB=\angle ADB=\frac{70{}^\circ }{2}=35{}^\circ $

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