SSC CGL 2014 Tier 1 20 July Second Sitting

Question 127

ABC is an isosceles triangle and AB-AC and D is a point on AC so that BD-DC if <ABD=<CBD then the measure of <BAC

Solution

From the description, it is clear that it is an isoscles triangle.
Let angle A = A.
Angle B + Angle C = 180 - A.
Let angle B be B.
Angle C = angle B = B.
2B = 180 - A.
=> B = 90-A/2.=> Angle ACB = 90 - A/2
Now, angle CBD = angle ABD.
Angle CBD = 45 - A/4.
But, we know that Angle ACB = Angle CBD.
=> 90 - A/2 = 45 - A/4.
45 = A/2.
A = 90 degrees.
B = 90/2 = 45 degrees.
Option C is the right answer.


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