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 $
BETA
