In the diagram above, AC = AB, and angle DAB = angle DBC. What is the

Question

https://gmatclub.com/forum/download/file.php?id=26290 In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD? (1) angle BDC = 2*(angle DAB) (2) AD = BD Kudos for a correct solution . gdrtq_img4.png

Lucky2783 · Answer

Answer D .

Naina1 · Answer

I'll go with C.

Given : AC=AB
this implies angle ABC=angle ACB
Let angle DAB=x=angle DBC

Condition 1: angle BDC=2*angle DAB=2x
 So, angle BCD=180-(x+2x)=180-3x
This could not help any further.

Condition 2: AD=BD
This gives angle DAB=angle DBA=x
This also is insufficient.

Both 1+2
As angle ABC=angle ACB
 angle DBA+angle DBC=angle ACB
 x+x=180-3x
 2x=180-3x
 5x=180
 x=36
So, angle BCD=180-3x=180-3*36=180-108=72

Lucky2783 · Answer

please see attached for option A. you can do the same for option B.

Naina1 · Answer

my bad..
yes each statement alone is sufficient.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

From the prompt, we know that triangle ABC is  isosceles , with AB = AC and angle ABC = angle DCB. Because angle DAB = angle DBC, and they share the angle at C, we know triangle BCD is similar to triangle ABC; therefore, triangle BCD must also be isosceles, with BC = BD and angle BDC = angle BCD. For simplicity, let’s say that

x = angle DAB = angle DBC

y = angle ABC = angle DCB = angle BDC

We know that (x + 2y) = 180°, and the prompt is asking for the value of y.

Statement #1:  angle BDC = 2*(angle DAB)

In other words, y = 2x. Then

x + 2y = x + 4x = 5x = 180°

This means x = 36° and y = 72°. This statement leads directly to the numerical value sought in the prompt. This statement, alone and by itself, is sufficient.

Statement #2:  AD = BD

This tell us that triangle ABD is also isosceles. This means that angle DAB = angle ABD. Think about angle ABD. That angle is the “leftover” between two angles we have already discussed:

angle ABD = (angle ABC) – (angle CBD) = y – x

Well, angle DAB = x, so if these two are equal, this means:

y – x = x

y = 2x

This turns out to be the exact same information that was given in statement #1, which we already know is full sufficient.

Answer = (D)

(BTW, more than you need to know for the GMAT, but these are Golden Triangles, because the ratio AB/BC equals the Golden Ratio! )

mikemcgarry · Answer

isosceles triangle.JPG In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD? Statement #1 : angle BDC = 2*(angle DAB) Statement #2 : AD = BD For a collection of 12 challenging DS practice questions, and the OE for this particular question, see: https://magoosh.com/gmat/2015/gmat-data- ... uestion-2/ Mike :-)

sudh · Answer

given  	riangle ABC  is an isosceles triangle
 AB = AC 
 \angle ABC = \angle ACB   = ? 
Let's assume  \angle ABC = \angle ACB = x; \angle CAB = \angle DBC = y

from the question stem:
 2x + y = 180  -----------------> (i)

Statement 1: 
 \angle BDC = 2*\angle DAB = 2*\angle DBC 
From  	riangle DBC x + 3y = 180  --------- (ii)
Solving (i) and (ii)
 x = 72; y = 36; \angle ACB = 72 
Sufficient

Statement 2: 
AD = BD,  	riangle ABD is isosceles, \angle ABD = \angle DAB =y 
So  \angle ABC = 2y 
 x + 3y = 180  ---------------------> (iii); same as (ii)
Solving (i) and (iii)
 x = 72; y = 36; \angle ACB = 72 
Sufficient

Answer D

VenoMfTw · Answer

Capture.JPG St 1: BDC = 2 (180 -2x) Sum of angles in triangle BDC = 180. On solving we get x =72 St 2: AD+BD .. angles opp to equal sides are equal. 180-2x= 3x-180 x=72

CEdward · Answer

I attached my drawing. Can someone explain what I am doing wrong? Totally lost on this one.

I designated BAC as x and DBC as x.

St1 says BDC = 2BAC ---> BDC = 2X

I don't quite understand how everybody is saying BAC is 180 - 2x...

The only angle that I see as 180 - 2x is BDA

bumpbot · Answer

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In the diagram above, AC = AB, and angle DAB = angle DBC. What is the

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