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The Official Guide For GMAT® Quantitative Review, 2ND Edition
In the figure above, if F is a point on the line that bisects angle ACD and the measure of angle DCF is x°, which of the following is true of x ?
(A) 90 <= x < 100
(B) 100 <= x < 110
(C) 110 <= x < 120
(D) 120 <= x < 130
(E) 130 <= x < 140
Untitled.png [ 13.24 KiB | Viewed 33103 times ]
_________________
In the figure above, if F is a point on the line that bisects angle ACD and the measure of angle DCF is x°, which of the following is true of x ?
(A) 90 <= x < 100
(B) 100 <= x < 110
(C) 110 <= x < 120
(D) 120 <= x < 130
(E) 130 <= x < 140
Problem Solving
Question: 7
Category: Geometry Angles
Page: 62
Difficulty: 550
Question: 7
Category: Geometry Angles
Page: 62
Difficulty: 550
GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project
Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.
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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.
We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.
Thank you!
Attachment:
Untitled.png [ 13.24 KiB | Viewed 33103 times ]
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Bunuel
F is a point on the line that bisects angle ACD
We're told that ∠ACD = 90°
So, if a line BISECTS ∠ACD, the two resulting angles are each 45°
Since 2 angles on a line add to 180°...
...we can write: x + 45° = 180°
Solve: x = 135°
Answer: E
Cheers,
Brent
General Discussion
SOLUTION
In the figure above, if F is a point on the line that bisects angle ACD and the measure of angle DCF is x°, which of the following is true of x ?
(A) 90 <= x <= 100
(B) 100 <= x <= 110
(C) 110 <= x <= 120
(D) 120 <= x <= 130
(E) 130 <= x <= 140
Untitled.png [ 13.55 KiB | Viewed 31144 times ]
Since line BF bisects angle ACD, then angle BCD is 90°/2=45°. Together with angle x they comprise a straight line, which implies that 45°+x=180°. Therefore x=135°.
Answer: E.
_________________
In the figure above, if F is a point on the line that bisects angle ACD and the measure of angle DCF is x°, which of the following is true of x ?
(A) 90 <= x <= 100
(B) 100 <= x <= 110
(C) 110 <= x <= 120
(D) 120 <= x <= 130
(E) 130 <= x <= 140
Attachment:
Untitled.png [ 13.55 KiB | Viewed 31144 times ]
Answer: E.
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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).
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).
WoundedTiger
Joined: 25 Apr 2012
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Attachment:
untitled1.PNG [ 9.78 KiB | Viewed 29393 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
Posts: 161
Hi GMATters,
Here is my video explanation of the problem. Enjoy!
Rowan
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Here is my video explanation of the problem. Enjoy!
Rowan
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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?
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?
adkikani
Hi adkikani
generally equal angles are represented by two similar "CURVED" lines. Here it is representing two perpendicular lines.
Gmatsaiyan
Joined: 05 Feb 2018
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Location: India
Concentration: Finance
GPA: 2.77
WE:General Management (Other)
Posts: 748
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
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