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Math Expert V
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In the figure above, if F is a point on the line that bisects angle AC  [#permalink]

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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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Math Expert V
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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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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 [ 13.55 KiB | Viewed 16048 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°.

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GMAT 1: 590 Q45 V27 Re: In the figure above, if F is a point on the line that bisects angle AC  [#permalink]

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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]

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Attachment: untitled1.PNG [ 9.78 KiB | Viewed 14818 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
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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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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]

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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?
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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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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.
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In the figure above, if F is a point on the line that bisects angle AC  [#permalink]

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1 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
_________________ In the figure above, if F is a point on the line that bisects angle AC   [#permalink] 14 Oct 2018, 09:08
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