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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In the diagram above, AC = AB, and angle DAB = angle DBC. What is the

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Math Expert V
Joined: 02 Sep 2009
Posts: 64083
In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 59% (02:39) correct 41% (02:57) wrong based on 143 sessions

### HideShow timer Statistics In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

Kudos for a correct solution.

Attachment: gdrtq_img4.png [ 8.74 KiB | Viewed 66382 times ]

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Senior Manager  Joined: 07 Aug 2011
Posts: 490
GMAT 1: 630 Q49 V27
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Bunuel wrote: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

Kudos for a correct solution.

Attachment:
The attachment gdrtq_img4.png is no longer available

Attachments gmatclub.jpg [ 43.18 KiB | Viewed 47204 times ]

Intern  Joined: 05 Feb 2015
Posts: 46
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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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.

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
Senior Manager  Joined: 07 Aug 2011
Posts: 490
GMAT 1: 630 Q49 V27
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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1
Naina1 wrote:
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.

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

please see attached for option A. you can do the same for option B.
Attachments gmatclub.jpg [ 34.23 KiB | Viewed 47127 times ]

Intern  Joined: 05 Feb 2015
Posts: 46
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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yes each statement alone is sufficient.
Math Expert V
Joined: 02 Sep 2009
Posts: 64083
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Bunuel wrote: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

Kudos for a correct solution.

Attachment:
gdrtq_img4.png

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.

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.

(BTW, more than you need to know for the GMAT, but these are Golden Triangles, because the ratio AB/BC equals the Golden Ratio! )
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Magoosh GMAT Instructor G
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Posts: 4485
In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Attachment: isosceles triangle.JPG [ 16.07 KiB | Viewed 46827 times ]

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)

For a collection of 12 challenging DS practice questions, and the OE for this particular question, see:
http://magoosh.com/gmat/2015/gmat-data- ... uestion-2/

Mike _________________
Mike McGarry
Magoosh Test Prep

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Manager  Joined: 15 May 2014
Posts: 61
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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given $$\triangle ABC$$ 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 $$\triangle DBC x + 3y = 180$$ --------- (ii)
Solving (i) and (ii)
$$x = 72; y = 36; \angle ACB = 72$$
Sufficient

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

Manager  B
Joined: 14 Mar 2014
Posts: 139
GMAT 1: 710 Q50 V34
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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Bunuel wrote: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the measure of angle BCD?

(1) angle BDC = 2*(angle DAB)

Kudos for a correct solution.

Attachment:
The attachment gdrtq_img4.png is no longer available

Attachment: Capture.JPG [ 31.76 KiB | Viewed 45463 times ]

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
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Posts: 14970
Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the  [#permalink]

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_________________ Re: In the diagram above, AC = AB, and angle DAB = angle DBC. What is the   [#permalink] 07 Aug 2019, 19:40

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