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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  [#permalink]

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Updated on: 17 Jun 2017, 14:07
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2018.OG.05.026.q.png [ 32.11 KiB | Viewed 14366 times ]

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°

Originally posted by AbdurRakib on 17 Jun 2017, 11:21.
Last edited by Bunuel on 17 Jun 2017, 14:07, edited 1 time in total.
Renamed the topic and edited the question.
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In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

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Updated on: 16 Apr 2018, 12:40
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AbdurRakib wrote:
Attachment:
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°

If AC = 2 and DC = 1, then we can conclude that AD = 1
Add this information to the diagram...

If AD = 1 and BD = 1, then ∆ABD is an ISOSCELES triangle, which means ∠DAB = ∠ABD are EQUAL...

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

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Originally posted by GMATPrepNow on 03 Jul 2017, 12:14.
Last edited by GMATPrepNow on 16 Apr 2018, 12:40, edited 1 time in total.
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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

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17 Jun 2017, 11:27
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AbdurRakib wrote:
Attachment:
2018.OG.05.026.q.png
A. 15°
B. 20°
C. 30°
D. 40°
E. 45°

Given BD = DC = 1

AC = 2.

$$\triangle$$ ABD and $$\triangle$$ BDC are isosceles triangles.

$$\triangle$$ 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)...
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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

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03 Jul 2017, 12:22
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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

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04 Jul 2017, 02:55
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)
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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

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04 Jul 2017, 10:22
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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

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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

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15 Nov 2017, 16:46
AbdurRakib wrote:
Attachment:
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°

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

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

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27 Sep 2019, 08:16
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:
Attachments

aaa.PNG [ 249.06 KiB | Viewed 1563 times ]

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In the figure shown, AC = 2 and BD = DC = 1. What is the measure of   [#permalink] 27 Sep 2019, 08:16
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