GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Aug 2019, 04:40

### 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

# In the diagram above, angles GAF, FBE, and ECD are all equal in measur

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Aug 2013
Posts: 94
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)
In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

Updated on: 31 Dec 2017, 14:13
1
28
00:00

Difficulty:

95% (hard)

Question Stats:

45% (02:28) correct 55% (02:51) wrong based on 121 sessions

### HideShow timer Statistics

In the diagram above, angles GAF, FBE, and ECD are all equal in measure. If line AG is the diameter of the circle and parallel to lines BF and CE, what is the measure of angle CFB?

A. 15
B. 20
C. 25
D. 30
E. 35

Attachment:

Untitled.png [ 14.45 KiB | Viewed 6395 times ]

Originally posted by anceer on 04 Dec 2014, 05:44.
Last edited by Bunuel on 31 Dec 2017, 14:13, edited 2 times in total.
Edited the question.
Intern
Joined: 24 Apr 2013
Posts: 15
Location: Russian Federation
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

05 Dec 2014, 07:42
4
3
Let "O" be the center of the circle
Angle AOG=180

Arcs GF=FE=ED=DC=CD=BA
Total: 6 arcs
180/6=30

So angles GOF=FOE=EOD=DOC=COB=BOA=30

Inscribed angles measure half of their corresponding central angles = 30/2 = 15
##### General Discussion
Manager
Joined: 04 Aug 2013
Posts: 94
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

05 Dec 2014, 05:59
The OE
Can any one explain it..

A. This problem relies heavily on the concepts of inscribed and central angles. If all the inscribed angles in the figure (GAF, FBE, ECD, and their "opposite" angles across the circle) are the same measurement, then there are 6 identical inscribed angles in the semicircle. Now, consider if each arclength - AB, BC, CD, etc. - were created by central angles. That would be six 30-degree angles from the center of the circle, and since inscribed angles measure half of their corresponding central angles, that means that the inscribed angles are 15 degrees, making A the correct answer.
Manager
Joined: 06 Mar 2014
Posts: 86
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

22 Dec 2014, 04:58
Hi,

Can any1 please explain why are all arcs equal??
And why are all angles equal??
Manager
Joined: 04 Aug 2013
Posts: 94
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

29 Dec 2014, 20:38
1
Shree9975 wrote:
Hi,

Can any1 please explain why are all arcs equal??
And why are all angles equal??

All 3 lines are parallel, and the internal angel FAG EBF and DCE are equal.
so the other 3 angle must be identical
(just for clear understanding take the section ABFG.
you know the distance between AF and BG are equal as BF // AG
so the angle made by BG on AG must be equal to the angle made by FA on AG)
When angles are same the arc must be same...

hope you got it
Manager
Joined: 03 May 2013
Posts: 67
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

07 Jun 2015, 22:22
1
anceer wrote:
Shree9975 wrote:
Hi,

Can any1 please explain why are all arcs equal??
And why are all angles equal??

All 3 lines are parallel, and the internal angel FAG EBF and DCE are equal.
so the other 3 angle must be identical
(just for clear understanding take the section ABFG.
you know the distance between AF and BG are equal as BF // AG
so the angle made by BG on AG must be equal to the angle made by FA on AG)
When angles are same the arc must be same...

hope you got it

OK now what, this is how you got AB = FG , and BC = EF , but how AB=BC = CD possible??
Intern
Joined: 15 Sep 2012
Posts: 8
Location: India
Concentration: Operations, Technology
GMAT 1: 500 Q41 V19
GPA: 2.9
WE: Information Technology (Consulting)
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

05 Mar 2016, 19:17
because these lines are parallel to each other.

vipulgoel wrote:
anceer wrote:
Shree9975 wrote:
Hi,

Can any1 please explain why are all arcs equal??
And why are all angles equal??

All 3 lines are parallel, and the internal angel FAG EBF and DCE are equal.
so the other 3 angle must be identical
(just for clear understanding take the section ABFG.
you know the distance between AF and BG are equal as BF // AG
so the angle made by BG on AG must be equal to the angle made by FA on AG)
When angles are same the arc must be same...

hope you got it

OK now what, this is how you got AB = FG , and BC = EF , but how AB=BC = CD possible??
Manager
Joined: 25 Apr 2016
Posts: 59
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

23 May 2017, 05:13
as per the given question stem each of the six arch would make equal angle at the circumference of the circle that implies the archs are of equal length. Angle each of them formed at the center must also be equal, which implies each formed an angle of 180/6 degrees and angle formed at the center is double the angle formed at the circumference, and importantly, required angle is at the circumference => angle CFB =180 /6*2= 15 degress -> option A
Senior Manager
Joined: 03 Apr 2013
Posts: 268
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

17 Nov 2017, 06:55
anceer wrote:
Attachment:
Untitled.png
In the diagram above, angles GAF, FBE, and ECD are all equal in measure. If line AG is the diameter of the circle and parallel to lines BF and CE, what is the measure of angle CFB?

A. 15
B. 20
C. 25
D. 30
E. 35

Bunuel
VeritasPrepKarishma please confirm, is D placed exactly in the middle of the semicircle? If yes then I have a solution. But before I discuss my solution that took me like years to figure out, please share your explanations and related concepts. Thanks a lot
_________________
Spread some love..Like = +1 Kudos
Math Expert
Joined: 02 Sep 2009
Posts: 57237
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

31 Dec 2017, 14:13
anceer wrote:

In the diagram above, angles GAF, FBE, and ECD are all equal in measure. If line AG is the diameter of the circle and parallel to lines BF and CE, what is the measure of angle CFB?

A. 15
B. 20
C. 25
D. 30
E. 35

Attachment:
Untitled.png

VERITAS PREP OFFICIAL SOLUTION:

A. This problem relies heavily on the concepts of inscribed and central angles. If all the inscribed angles in the figure (GAF, FBE, ECD, and their "opposite" angles across the circle) are the same measurement, then there are 6 identical inscribed angles in the semicircle. Now, consider if each arclength - AB, BC, CD, etc. - were created by central angles. That would be six 30-degree angles from the center of the circle, and since inscribed angles measure half of their corresponding central angles, that means that the inscribed angles are 15 degrees, making A the correct answer.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7420
Location: United States (CA)
Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur  [#permalink]

### Show Tags

05 Aug 2019, 19:20
anceer wrote:

In the diagram above, angles GAF, FBE, and ECD are all equal in measure. If line AG is the diameter of the circle and parallel to lines BF and CE, what is the measure of angle CFB?

A. 15
B. 20
C. 25
D. 30
E. 35

Attachment:
Untitled.png

We see that angles GAF, FBE, and ECD are inscribed angles, and their respective intercepted arcs are FG, EF and DE. Since angle GAF = angle FBE = angle ECD, arc FG = arc EF = arc DE. We see that arc DG is a quarter circle, which is 90 degrees; therefore, arc FG = arc EF = arc DE = 30 degrees. Since an inscribed angle is half its intercepted arc, angle GAF = angle FBE = angle ECD = 15 degrees. Since angle CFB = angle FBE, angle CFB = 15 degrees.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In the diagram above, angles GAF, FBE, and ECD are all equal in measur   [#permalink] 05 Aug 2019, 19:20
Display posts from previous: Sort by

# In the diagram above, angles GAF, FBE, and ECD are all equal in measur

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne