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If A, B, C, D, and E are points in a plane such that line CD

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If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   30 Sep 2018, 02:39
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If A, B, C, D, and E are points in a plane such that line CD bisects ∠ACB and line CB bisects right angle ∠ACE, then ∠DCE =

(A) 22.5°
(B) 45°
(C) 57.5°
(D) 67.5°
(E) 72.5°
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D
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   01 Oct 2018, 04:05
explain pls??
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   01 Oct 2018, 07:50
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Quote:
CD bisects ∠ ACB
CB bisects ∠ ACE

We are given that CB bisects the right-angle ∠ ACE. Hence, ∠ ACB = ∠ BCE = ∠ ACE/2 = 90°/2 = 45°. Also, since CD bisects ∠ ACB, ∠ ACD = ∠ D C B = ∠ ACB/2 = 45°/2 = 22.5°. Now, ∠ DCE =
∠ DCB + ∠ BCE = 22.5° + 45° = 67.5°. The answer is (D).


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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   13 Dec 2018, 16:06
Can someone please explain with pictures?
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   15 Dec 2018, 01:23
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QuantumWonder wrote:
Can someone please explain with pictures?


The picture is self explanatory

Attachment:
image.jpg
image.jpg [ 134.41 KiB | Viewed 5636 times ]
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   15 Dec 2018, 17:14
sandy wrote:
QuantumWonder wrote:
Can someone please explain with pictures?


The picture is self explanatory

Attachment:
image.jpg


Thank you!
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   09 Jun 2020, 10:44
Hello,I have a question, how do we know that Angle ACE is a right angle?
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   09 Jun 2020, 11:01
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If A, B, C, D, and E are points in a plane such that line CD bisects ∠ACB and line CB bisects right angle ∠ACE, then ∠DCE =

Right angle = 90°

Hope this helps
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   12 Aug 2022, 06:15
sandy wrote:
QuantumWonder wrote:
Can someone please explain with pictures?


The picture is self explanatory

Attachment:
image.jpg


Thank you so much for this
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Re: If A, B, C, D, and E are points in a plane such that line CD [#permalink] New post   07 Nov 2023, 16:29
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