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

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Bunuel
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In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   26 Dec 2013, 08:52
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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

Problem Solving
Question: 7
Category: Geometry Angles
Page: 62
Difficulty: 550


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BrentGMATPrepNow
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   09 Mar 2020, 07:40
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Bunuel wrote:
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


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
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   26 Dec 2013, 08:53
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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

Attachment:
Untitled.png
Untitled.png [ 13.55 KiB | Viewed 29321 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.
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   26 Dec 2013, 22:24
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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).
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   30 Dec 2013, 05:25
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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
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   08 May 2017, 05:06
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Hi GMATters,

Here is my video explanation of the problem. Enjoy!



Rowan
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   15 Jun 2018, 04:32
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?
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   15 Jun 2018, 05:04
adkikani wrote:
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?


Hi adkikani

generally equal angles are represented by two similar "CURVED" lines. Here it is representing two perpendicular lines.
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In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   14 Oct 2018, 09:08
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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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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink] New post   16 Nov 2022, 03:00
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Re: In the figure above, if F is a point on the line that bisects angle AC [#permalink]
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