CAT 2015 Quantitative Ability

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Question : 2 of 34

Marks: +1, -0

In the given figure, AB is the diameter of the circle with centre O. If ∠BOD = 15°, ∠EOA = 85°, then find the measure of ∠ECA.

20°
25°
35°
Cannot be determined

Solution:

∠\text"EOA" =85°

∠\text"BOD" =15°

∴ \;\; ∠\text"EOD" =180° - (85° + 15°) = 80°

∴ In ∆OED
OE = OD(radius)

∴ \;\;∠\text"OED" = ∠\text"ODE" =50°

In ∆EOC,

∠\text"EOC" =80° + 15° =95°

and

∠\text"OEC" =50°

∠\text"ECA" =180° - (95° + 50°) = 35°

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