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# In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, an

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, an  [#permalink]

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13 Jan 2019, 23:58
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Difficulty:

15% (low)

Question Stats:

97% (01:09) correct 3% (02:09) wrong based on 40 sessions

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In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, and BC = 4, what is the length of BD ?

A. $$\sqrt{2}$$

B. 4

C. $$4\sqrt{2}$$

D. $$4\sqrt{3}$$

E. 8

Attachment:

2019-01-14_1048.png [ 19.54 KiB | Viewed 480 times ]

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Posts: 5014
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, an  [#permalink]

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14 Jan 2019, 03:56
Bunuel wrote:

In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, and BC = 4, what is the length of BD ?

A. $$\sqrt{2}$$

B. 4

C. $$4\sqrt{2}$$

D. $$4\sqrt{3}$$

E. 8

Attachment:
2019-01-14_1048.png

angle dbc = 120

angle bdc = 30
side bc=bd
IMO B 4
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, an  [#permalink]

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14 Jan 2019, 04:28
Bunuel wrote:

In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, and BC = 4, what is the length of BD ?

A. $$\sqrt{2}$$

B. 4

C. $$4\sqrt{2}$$

D. $$4\sqrt{3}$$

E. 8

Attachment:
2019-01-14_1048.png

Note that exterior angle = Sum of interior opposite angles

Angle ABD = angle BCD + angle BDC
60 = 30 + angle BDC

Angle BDC = 30 degrees

This means triangle BDC is isosceles with BC = BD

Since BC = 4, hence BD = 4

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Karishma
Veritas Prep GMAT Instructor

Re: In the figure above, if ∠DBA has measure 60°, ∠DCB has measure 30°, an   [#permalink] 14 Jan 2019, 04:28
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