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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 11418 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°

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Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

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

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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of   [#permalink] 10 Mar 2019, 22:57
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