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In the figure above, if F is a point on the line that bisect

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In the figure above, if F is a point on the line that bisect [#permalink] New post   21 May 2020, 09:11
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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
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E
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Re: In the figure above, if F is a point on the line that bisect [#permalink] New post   21 May 2020, 09:11
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Re: In the figure above, if F is a point on the line that bisect [#permalink] New post   21 May 2020, 09:20
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Carcass wrote:
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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°
Image


Since 2 angles on a line add to 180°...
Image
...we can write: x + 45° = 180°
Solve: x = 135°

Answer: E

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Re: In the figure above, if F is a point on the line that bisect [#permalink] New post   23 May 2020, 05:02
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In above figure since line CF bisects angle ACD

angle ACK = angle DCK = \(\frac{1}{2}\) * 90 = 45

Now CF is straight line angle KCD + angle FCD = 180

45 + x = 180

x = 135

Answer is E
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Re: In the figure above, if F is a point on the line that bisect [#permalink] New post   27 May 2020, 02:46
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Re: In the figure above, if F is a point on the line that bisect [#permalink] New post   20 Feb 2023, 10:23
Hello from the GRE Prep Club BumpBot!

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Re: In the figure above, if F is a point on the line that bisect [#permalink]
20 Feb 2023, 10:23
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