SATHEE: Quantitative Aptitude Ques 2117

Quantitative Aptitude Ques 2117

Question: In the adjoining figure, AB is a diameter of the circle with centre O. If $ \angle BOD=15{}^\circ $ and $ \angle EOA=85{}^\circ , $ then the measure of $ \angle ECA $ is

Options:

A) $ 45{}^\circ $

B) $ 35{}^\circ $

C) $ 30{}^\circ $

D) $ 70{}^\circ $

Show Answer

Answer:

Correct Answer: B

Solution:

$ \angle AOB=180{}^\circ $

$ \Rightarrow $ $ \angle AOE+\angle EOD+\angle DOB=180{}^\circ $ (by angle sum property)

$ \Rightarrow $ $ 85{}^\circ +\angle EOD+15{}^\circ =180{}^\circ $ $ \angle EOD=80{}^\circ $ $ \because $ $ OD=OE $ [radius of circle]

$ \therefore $ $ \angle OED=\angle ODE=\frac{180{}^\circ -\angle EOD}{2} $ $ =\frac{180{}^\circ -80{}^\circ }{2}=50{}^\circ $ $ [\because OE=OD] $

$ \therefore $ $ \angle ODC=180{}^\circ -\angle ODE=130{}^\circ $ Now, in $ \Delta DOC, $ $ \angle ODC+\angle DOC+\angle DCO=180{}^\circ $ $ 130{}^\circ +15{}^\circ +\angle DCO=180{}^\circ $

$ \Rightarrow $ $ \angle DCO=35{}^\circ $ $ \angle ECA=35{}^\circ $

Quantitative Aptitude Ques 2116

Quantitative Aptitude Ques 2118

Quantitative Aptitude Ques 2117

Question: In the adjoining figure, AB is a diameter of the circle with centre O. If $ \angle BOD=15{}^\circ $ and $ \angle EOA=85{}^\circ , $ then the measure of $ \angle ECA $ is

Options:

Answer:

Solution:

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