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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If A, B, C, D, and E are points in a plane such that line CD bisects  [#permalink]

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09 Oct 2018, 20:41
00:00

Difficulty:

45% (medium)

Question Stats:

65% (02:08) correct 35% (02:26) wrong based on 30 sessions

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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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Joined: 19 Oct 2013
Posts: 508
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If A, B, C, D, and E are points in a plane such that line CD bisects  [#permalink]

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10 Oct 2018, 10:02
1
Bunuel wrote:
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°

Angle ACE = 90 degree since CB bisects ACE then

BCE = 45 degree

ACB = 45 degree. Since CD bisects ACB

We get two angles ACD = 45/2 = 22.5 and DCB = 45/2 = 22.5

DCE = DCB + BCE = 22.5 + 45 = 67.5

Attachments

Screen Shot 2018-10-10 at 9.11.21 PM.png [ 24.5 KiB | Viewed 349 times ]

Manager
Joined: 03 Mar 2017
Posts: 248
Re: If A, B, C, D, and E are points in a plane such that line CD bisects  [#permalink]

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10 Oct 2018, 21:11
Salsanousi wrote:
Bunuel wrote:
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°

Angle ACE = 90 degree since CB bisects ACE then

BCE = 45 degree

ACB = 45 degree. Since CD bisects ACB

We get two angles ACD = 45/2 = 22.5 and DCB = 45/2 = 22.5

DCE = DCB + BCE = 22.5 + 45 = 67.5

Great Image!! That is a perfect explanation.
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Re: If A, B, C, D, and E are points in a plane such that line CD bisects   [#permalink] 10 Oct 2018, 21:11
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