Last visit was: 12 Aug 2024, 22:34 It is currently 12 Aug 2024, 22:34
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# In the figure above, if F is a point on the line that bisects angle AC

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649116 [18]
Given Kudos: 86922
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30998 [5]
Given Kudos: 799
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649116 [2]
Given Kudos: 86922
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 288 [2]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
1
Kudos
SOLUTION:

Assume an imaginary point B on the line between A and D. Since angle ACD is 90 and the line bisects ACD, angle ACB = angle DCB = 45.
Since a straight line has 180 degree,
angle BCD + x = 180
45 + x = 180
x = 135.

So, x lies between 130 and 140. Ans is (E).
Director
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2335 [0]
Given Kudos: 740
Location: India
GPA: 3.21
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
Attachment:

untitled1.PNG [ 9.78 KiB | Viewed 27979 times ]

Given that the line bisects the angle ACD which 90 deg so angle DCE is 45 deg.

Now 45 +Angle x= 180 by Linear Pair axiom so

Angle x= 135 and hence ans E
Tutor
Joined: 30 Oct 2012
Status:London UK GMAT Consultant / Tutor
Posts: 75
Own Kudos [?]: 157 [1]
Given Kudos: 3
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
1
Kudos
Hi GMATters,

Here is my video explanation of the problem. Enjoy!

Rowan
IIM School Moderator
Joined: 04 Sep 2016
Posts: 1249
Own Kudos [?]: 1268 [0]
Given Kudos: 1207
Location: India
WE:Engineering (Other)
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
Bunuel niks18 gmatbusters pushpitkc

i know that square symbol always represents a 90 degree angle in GMAT, here I was confused since angle BCA and angle BCD are also equal because of bisector.
Can the symbol in q stem not represent two bisecting angles?
Retired Moderator
Joined: 25 Feb 2013
Posts: 893
Own Kudos [?]: 1562 [0]
Given Kudos: 54
Location: India
GPA: 3.82
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
Bunuel niks18 gmatbusters pushpitkc

i know that square symbol always represents a 90 degree angle in GMAT, here I was confused since angle BCA and angle BCD are also equal because of bisector.
Can the symbol in q stem not represent two bisecting angles?

generally equal angles are represented by two similar "CURVED" lines. Here it is representing two perpendicular lines.
Director
Joined: 05 Feb 2018
Posts: 755
Own Kudos [?]: 2328 [1]
Given Kudos: 139
Location: India
Concentration: Finance
GPA: 2.77
WE:General Management (Other)
In the figure above, if F is a point on the line that bisects angle AC [#permalink]
1
Kudos

Given angle DCA = 90 degrees

Also we know that
angle DCA + angle DCF + angle ACF=360 degrees (Internal + External angles)

90 degrees + angle DCF + angle ACF=360 degrees
angle DCF + angle ACF=270 degrees

(since angle bisector angle DCF = angle ACF )
2x= 270 degrees
Thus x= 135 degrees
Non-Human User
Joined: 09 Sep 2013
Posts: 34396
Own Kudos [?]: 862 [0]
Given Kudos: 0
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
Moderator:
Math Expert
94906 posts