In the triangle above, what is the measure of Angle CDB?

[BTGmoderatorDC]

In the triangle above, what is the measure of Angle CDB?
(1) Angle CAB = Angle ACB = 30°
(2) AB = BC = BD


OA A


Source: e-GMAT

[Jay@ManhattanReview]

Screen-Shot-2016-11-22-at-5.28.41-PM-e1479816030549.png

In the triangle above, what is the measure of Angle CDB?

(1) Angle CAB = Angle ACB = 30°
(2) AB = BC = BD

OA A

Source: e-GMAT

Let's take each statement one by one.

(1) Angle CAB = Angle ACB = 30°

Given that Angle CAB = Angle ACB = 30°, in the ∆ABC, we have Angle ABC = 180 – 30 – 30 = 120º.

Also, since Angle ACD = 90º and Angle CAB = 30º, we have Angle BCD = 90 – 30 = 60º

Also, since Angle ABC = 120º, we have Angle CBD = 60º.

So, in ∆BCD, Angle CDB = 180 – 60 – 60 = 60º

Sufficient.

(2) AB = BC = BD

Since we do not have any measure of angles, we cannot get the unique value of Angle CDB. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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