Triangle problem

[1uponGMAT]

How would you all go about solving this? At first I thought that the larger ABC triangle was 30-60-90, but I am not sure about this. Thanks!


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[niksworth]

Angle BDC = Angle BCD = 2x
=> Triangle BDC is isosceles
=> BD = BC --------------(1)

In a triangle, exterior angle is equal to the sum of interior angles.
So, Angle BDC = Angle Angle ABD + Angle BAD
=> 2x = Angle ABD + x
=> Angle ABD = x
=> Triangle ABD is isosceles
=> AD = BD --------------(1)

From (1) and (2)
AD = BD = BC ------------(3)

Q. What is BC?

Statement 1
AD = 6
=> BC = 6 (From 3)

Sufficient.

Statement 2
x=36.

This itself is insufficient as AD can take any value without disturbing the angle.

Insufficient.

Answer A

[1uponGMAT]

thank you for this:

In a triangle, exterior angle is equal to the sum of interior angles.
So, Angle BDC = Angle Angle ABD + Angle BAD

will have to review that section of the Geometry curriculum.

Thanks again!

[Brent@GMATPrepNow]

Thought it might help to draw this one out.

[GMATGuruNY]

To determine how the angles in a figure affect each other, plug in for the angle measurements, following the rules of geometry and the conditions given in the problem:



The drawings above show two combinations of angles that follow both the rules of geometry and the conditions given in the problem.
In each case, AD = BD = BC.

Question rephrased: What is the length of AD or BD?

Statement 1: AD = 6.
Sufficient.

Statement 2: x=36.
No information about the any of the lengths.
Insufficient.

The correct answer is A.

[venmic]

Hi -
I do not understand how is AD = BD = BC
I understand how AD = BD but NOT how it is equal to BC from the angles.
Even from the picture I dont see how it is equal

Appreciate it if you can explain

Thanks

To determine how the angles in a figure affect each other, plug in for the angle measurements, following the rules of geometry and the conditions given in the problem:



The drawings above show two combinations of angles that follow both the rules of geometry and the conditions given in the problem.
In each case, AD = BD = BC.

Question rephrased: What is the length of AD or BD?

Statement 1: AD = 6.
Sufficient.

Statement 2: x=36.
No information about the any of the lengths.
Insufficient.

The correct answer is A.

[GMATGuruNY]

Hi -
I do not understand how is AD = BD = BC
I understand how AD = BD but NOT how it is equal to BC from the angles.
Even from the picture I dont see how it is equal

Appreciate it if you can explain

Thanks

In each of the drawings above:
In ∆ABD, ∠BAD = ∠ABD. Thus, AD = BD.
In ∆BCD, ∠BDC = ∠BCD. Thus, BD = BC.
Since AD = BD and BD = BC, we know that AD = BD = BC.