Last visit was: 13 Sep 2026, 10:46 It is currently 13 Sep 2026, 10:46
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 13 Sep 2026
Posts: 113,480
Own Kudos:
841,049
 [2]
Given Kudos: 111,490
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,480
Kudos: 841,049
 [2]
If A, B, C, D, and E are points in a plane such that line CD bisects 09 Oct 2018, 21:41
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

66% (02:01) correct 34% (02:12) wrong based on 92 sessions

History

Date
Time
Result
Not Attempted Yet
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°
ShowHide Answer
Official Answer
D
User avatar
Salsanousi
User avatar
Joined: 19 Oct 2013
Last visit: 29 Dec 2020
Posts: 390
Own Kudos:
360
 [2]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Posts: 390
Kudos: 360
 [2]
If A, B, C, D, and E are points in a plane such that line CD bisects 10 Oct 2018, 11:02
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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°
Show more

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

Answer choice D
Attachments

Screen Shot 2018-10-10 at 9.11.21 PM.png
Screen Shot 2018-10-10 at 9.11.21 PM.png [ 24.5 KiB | Viewed 6944 times ]

User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Own Kudos:
440
Given Kudos: 596
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 537
Kudos: 440
If A, B, C, D, and E are points in a plane such that line CD bisects 10 Oct 2018, 22:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Salsanousi
Bunuel
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

Answer choice D
Show more

Great Image!! That is a perfect explanation.
avatar
Ayush Mishra
avatar
Joined: 08 Jan 2016
Last visit: 30 Jun 2022
Posts: 6
Given Kudos: 3
GMAT 1: 600 Q49 V23
GPA: 3.5
Products:
My Reviews
GMAT 1: 600 Q49 V23
Posts: 6
Kudos: 0
If A, B, C, D, and E are points in a plane such that line CD bisects 02 Mar 2020, 12:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Where is it written that angle ACE is right angle??

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,228
Own Kudos:
1,158
Posts: 39,228
Kudos: 1,158
If A, B, C, D, and E are points in a plane such that line CD bisects 17 Oct 2025, 02:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113480 posts