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Math Expert V
Joined: 02 Sep 2009
Posts: 56350
In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 80% (02:47) correct 20% (02:30) wrong based on 49 sessions

### HideShow timer Statistics  In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?

A. 25
B. 35
C. 45
D. 55
E. 65

Attachment: Capture.PNG [ 7.58 KiB | Viewed 667 times ]

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Intern  B
Joined: 10 May 2019
Posts: 7
GPA: 3.9
WE: Corporate Finance (Commercial Banking)
Re: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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Given info:
1) BC = CD = BD
2) angle FED = 40
3) angle EFD = 75
4) BG || DF

Using (1), angles cbd=bcd=bdc=60
Using (2) and (4), and applying concept of Vertically opposite angles:
angle D made by line segment CD is 40.
Angle between extended DF and BD is 60+40 = 100

Applying sum of interior angles on same transverse is 180
Therefore, upper angle B and D sum to 180
angle B + D = 180
=> B= 180-100 = 80

Now, angle B (made by extended line segment BG and CB):
= 80-60 = 20

Again, applying vertically opposite angles:
angle ABG = 20

From (3) and (4);
angle DFE = BGF = 75

angle BGA = 180 - 75 = 105

therefore, angle BAG = 180 - 105 - 20 = 55

Senior Manager  G
Joined: 22 Nov 2018
Posts: 485
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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1
Bunuel wrote: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?

A. 25
B. 35
C. 45
D. 55
E. 65

Attachment:
Capture.PNG

Find Angle E using sum of angles in a triangle rule = E=65.
angle C=60 as CBD is equilateral triangle (from stem: BC = CD = BD)
So using sum of angles in a triangle rule ACE arrive at angle A 60+65+A=180; A=55 IMO D
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Intern  B
Joined: 30 May 2017
Posts: 32
Concentration: Marketing, General Management
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Re: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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In this Question, the only property that is to be used is Sum of triangles.

Triangle BCD is an equilateral triangle, hence all the angles are 60. then in triangle, DFE, angle E = 180-75-40, ie., 65
so, triangle AEC, A = 180-65-60
180-125 = 55 ie. D +KUDOS, if you like the answer.
Director  G
Joined: 20 Jul 2017
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Re: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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Bunuel wrote: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?

A. 25
B. 35
C. 45
D. 55
E. 65

Attachment:
Capture.PNG

In Triangle DEF, LE +LF + LD = 180
--> LE + 75 + 40 = 180
--> LE = 65

Triangle BCD is Equilateral --> LC = 60

In Triangle ACE, LA + LC + LE = 180
--> LA + 60 + 65 = 180
--> L = 180 - 125 = 55

IMO Option D

Pls Hit Kudos if you like the solution
GMAT Club Legend  D
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Posts: 4261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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Bunuel wrote: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?

A. 25
B. 35
C. 45
D. 55
E. 65

Attachment:
Capture.PNG

other side angle is 65 and ∆ BCD is equilateral so 60
180-60+65; 55
angle A is 55
IMO D
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Posts: 4512
Location: India
GPA: 3.5
Re: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  [#permalink]

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Bunuel wrote: In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?

A. 25
B. 35
C. 45
D. 55
E. 65

Attachment:
Capture.PNG

1. Since in △BCD , BC = CD = BD, its an equilateral Triangle and ∠CBD = ∠BDC = ∠BCD = 60°
2. In △DEF , ∠DEF= 180° - (40° + 75°) => 65°
3. In △ACE, ∠CAE = 180° - (60° + 65°) => 55°

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Abhishek....

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# In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and li  