It is currently 14 Dec 2017, 05:28

# Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 563

Kudos [?]: 3057 [2], given: 220

GPA: 2.81
In the figure shown, AC = 2 and BD = DC = 1. What is the measure of [#permalink]

### Show Tags

17 Jun 2017, 10:21
2
KUDOS
Top Contributor
1
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:20) correct 11% (01:55) wrong based on 293 sessions

### HideShow timer Statistics

Attachment:

2018.OG.05.026.q.png [ 32.11 KiB | Viewed 2217 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°
[Reveal] Spoiler: OA

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Last edited by Bunuel on 17 Jun 2017, 13:07, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 3057 [2], given: 220

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 339 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of [#permalink]

### Show Tags

17 Jun 2017, 10:27
1
This post was
BOOKMARKED
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)...

Kudos [?]: 339 [0], given: 261

SVP
Joined: 11 Sep 2015
Posts: 1908

Kudos [?]: 2749 [2], given: 364

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

### Show Tags

03 Jul 2017, 11:14
2
KUDOS
Expert's post
Top Contributor
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

RELATED VIDEOS

_________________

Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2749 [2], given: 364

Manager
Joined: 23 May 2017
Posts: 161

Kudos [?]: 56 [1], given: 7

Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of [#permalink]

### Show Tags

03 Jul 2017, 11:22
1
KUDOS
Attachment:

FullSizeRender (6).jpg [ 44.9 KiB | Viewed 1727 times ]

+ 30
_________________

If you like the post, please award me Kudos!! It motivates me

Kudos [?]: 56 [1], given: 7

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1702

Kudos [?]: 750 [0], given: 20

Location: India
WE: Sales (Retail)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of [#permalink]

### Show Tags

04 Jul 2017, 01:55
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)
_________________

Stay hungry, Stay foolish

Kudos [?]: 750 [0], given: 20

Senior Manager
Joined: 22 Nov 2016
Posts: 251

Kudos [?]: 64 [0], given: 42

Location: United States
GPA: 3.4
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of [#permalink]

### Show Tags

04 Jul 2017, 09:22

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

_________________

Kudosity killed the cat but your kudos can save it.

Kudos [?]: 64 [0], given: 42

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1940

Kudos [?]: 1018 [0], given: 3

Location: United States (CA)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of [#permalink]

### Show Tags

15 Nov 2017, 15:46
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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1018 [0], given: 3

Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of   [#permalink] 15 Nov 2017, 15:46
Display posts from previous: Sort by