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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:

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]
Attachment:
untitled1.PNG
untitled1.PNG [ 9.78 KiB | Viewed 27856 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!



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