In the figure shown, AC = 2 and BD = DC = 1. What is the measure of

Question

2018.OG.05.026.q.png In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD? A. 15° B. 20° C. 30° D. 40° E. 45°

BrentGMATPrepNow · Accepted Answer

If AC = 2 and DC = 1, then we can conclude that AD = 1
Add this information to the diagram...
 https://i.imgur.com/vcguoNo.png

If AD = 1 and BD = 1, then ∆ABD is an ISOSCELES triangle, which means ∠DAB = ∠ABD are EQUAL...
 https://i.imgur.com/Bhb0YBP.png

If we let x = BOTH ∠DAB and ∠ABD, then we can use the fact that angles in a triangle add to 180º
We can write: x + x + 120 = 180
Simplify: 2x + 120 = 180
Solve: x = 30

In other words, ∠ABD = 30º

Answer: C

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Leo8 · Answer

FullSizeRender (6).jpg + 30

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=dELHQtZCAbk

sashiim20 · Answer

Given BD = DC = 1

AC = 2.

AC = AD + DC => 2 = AD - 1

Therefore AD = 1

riangle  ABD and  	riangle  BDC are isosceles triangles.

riangle  ABD is isosceles, sides AD = BD = 1. Therefore  \angle  BAD =  \angle  ABD. Let this angle be x.

Given  \angle  ADB is  120^{\circ}

\angle  ADB +  \angle  BAD +  \angle  ABD = 180

120 + x + x = 180

2x = 180 - 120 = 60

x = \frac{60}{2} = 30^{\circ} . Answer (C)...

pushpitkc · Answer

Angle BDC is 60 degree (because the angle in a straight line is equal to 180 degree) 
Since BD = DC(as given in the question stem) the triangle must be equilateral.
Therefere DC=1.

Since AC=2, AD = AC - DC = 1
Angle ABD = Angle DAB = x (Angles opposite equal sides are equal)

We know that the sum of angles in a triangle is 180 degree,
2x + 120 = 180
 Angle ABD(x) = 30 degree(Option C)

sasyaharry · Answer

AC-DC=AD
AD = 1, this makes triangle ADC an isosceles triangle

Sum of interior opposite angles = exterior angle.
 \angle BAD + \angle ABD = \angle BDC 
Here these two angles are equal, lets say x.

Since AC is a straight line,  \angle BDC = 180^ {\circ} - 120^ {\circ} = 60^ {\circ}

Hence  \angle BAD + \angle ABD = 60^ {\circ} 
x+x=60
x=30

Answer is  C

ScottTargetTestPrep · Answer

Since AC = 2 and DC = 1, AD must be 1. Since BD = 1, this makes triangle ABD an isosceles triangle with angle D as the vertex angle and angles A and ABD as the base angles. We know that angles A and ABD are equal because the sides opposite them are equal. If we let each of the base angles = x, we can create the following equation:

x + x + 120 = 180

2x = 60

x = 30

Answer: C

chrtpmdr · Answer

Can someone help me, I have a flaw in my logic. 
I totally understand it, but I would have solved it from the second triangle.

Is it true that angles in the triangle on the right are 60 degree?

I somehow got stuck because I thought that if those angles are 60, the upper angle (aka the one we are looking for) has to be 120.
Is this wrong because it would only be 120 if I would draw a line from up there and the touch on the line would make it 180?

See drawing:

zvazviri · Answer

Are you saying angle ABC is 120 as well? That's where the error is. You can solve this many ways: the easy way is to realize that angle BDC is 60(linear pair). AC= 2 (given).If DC=1, then AD= 1 (AD+DB=AC). That means triangle ADB is an isosceles triangle with base angles DAB and DBA congruent. angle DAB + angle DBA+120=180. From there you get angle DBA is equal to 30 degrees.

Now if you wanted to use the triangle on the right, you have correctly deduced that the triangle on the right is equiangular. Note that segment BD is the median of triangle ABC. Since AD=BD=DC, we know that the triangle ABC is a right triangle. (the median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles. That means ABC is a right angle. Since DBC is 60 degrees, then ABD is 30 degrees.

bnppedro · Answer

What is the rule that I am missing? Wouldn't <ABD and <DAB have the same value as <BCD, <CBD and <BDA since they all share the same value on opposing legs?

MHIKER · Answer

As BD = DC = 1 and AC=2, so AD=1

Hence, Triangle ABD is an isosceles triangle, So, ABD angle =30

The answer is  C

MHIKER · Answer

BD = DC = 1 and AC=2, so AD=1

In triangle ABD, AD=BD=1 and This is an isosceles triangle.

Angle ADB=120 so ABD=DAB= \frac{60}{2} =30

The answer is C

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=9HoJWN5J5_A

bumpbot · Answer

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In the figure shown, AC = 2 and BD = DC = 1. What is the measure of

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In the figure shown, AC = 2 and BD = DC = 1. What is the measure of

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