Last visit was: 15 Sep 2026, 01:39 It is currently 15 Sep 2026, 01:39
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: 15 Sep 2026
Posts: 113,520
Own Kudos:
841,342
 [11]
Given Kudos: 111,536
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,520
Kudos: 841,342
 [11]
If DA = DB, CD = CB and AB = AC, then x= 09 Jul 2021, 01:30
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
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:

67% (02:28) correct 33% (02:34) wrong based on 90 sessions

History

Date
Time
Result
Not Attempted Yet

If DA = DB, CD = CB and AB = AC, then x=

A. 180/7
B. 30
C. 240/7
D. 36
E. 270/7


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
1.png
1.png [ 12.23 KiB | Viewed 3661 times ]
ShowHide Answer
Official Answer
A
User avatar
sumitkrocks
User avatar
Joined: 02 Jul 2017
Last visit: 22 Aug 2023
Posts: 636
Own Kudos:
888
 [2]
Given Kudos: 333
Location: India
Concentration: Strategy, Technology
Schools: IIMA PGPX'22 ISB'22 NUS '23 ESADE IESE '24 NTU
GMAT 1: 730 Q50 V39
GMAT 2: 710 Q50 V36
Products:
My Reviews
Schools: IIMA PGPX'22 ISB'22 NUS '23 ESADE IESE '24 NTU
GMAT 2: 710 Q50 V36
Posts: 636
Kudos: 888
 [2]
If DA = DB, CD = CB and AB = AC, then x= 09 Jul 2021, 02:18
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
7x = 180
x = 180/7
(A) is the correct answer IMO


Bunuel

If DA = DB, CD = CB and AB = AC, then x=

A. 180/7
B. 30
C. 240/7
D. 36
E. 270/7


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
1.png
Show more
avatar
kantapong
avatar
Joined: 20 Jun 2021
Last visit: 06 Sep 2026
Posts: 107
Own Kudos:
225
 [1]
Given Kudos: 4
Posts: 107
Kudos: 225
 [1]
If DA = DB, CD = CB and AB = AC, then x= 09 Jul 2021, 02:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Define angle BAC = x and angle BDC = y, and start labelling derived angles from these two variables.
Then, DBC = 180-2y = 180-(2x+y) = x+y (since AB = AC)
Therefore, y = 2x => 180 - 4x = 3x => x = 180/7 (A)
User avatar
asishron29181
User avatar
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Own Kudos:
553
 [1]
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
Posts: 185
Kudos: 553
 [1]
If DA = DB, CD = CB and AB = AC, then x= 09 Jul 2021, 09:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given,
DA = DB, CD = CB and AB = AC
We need to find value of x.
DA = DB
which implies angle DBA = x (isosceles triangle)
Now in triangle BDA,
x+x+ ADB = 180
ADB = 180 - 2x
angle BDC = 2x (supplementary angle)

Now in triangle BDC,
2x + 2x + BCD = 180
BCD = 180 -4x

Also given
AB = AC
angle ABC = angle ACB
3x = 180 -4x
7x = 180
x = 180/7

IMO A
User avatar
zanto
User avatar
Joined: 10 Jun 2021
Last visit: 14 Sep 2026
Posts: 10
Own Kudos:
10
 [3]
Given Kudos: 201
Posts: 10
Kudos: 10
 [3]
If DA = DB, CD = CB and AB = AC, then x= Updated on: 09 Jul 2021, 10:40
Originally posted by zanto on 09 Jul 2021, 09:33.
Last edited by zanto on 09 Jul 2021, 10:40, edited 1 time in total.
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have listed the steps in the picture attached. Choice A
Attachments

File comment: Drawing attempt
IMG-2042.jpg
IMG-2042.jpg [ 3.5 MiB | Viewed 3211 times ]

avatar
TarunKumar1234
avatar
Joined: 14 Jul 2020
Last visit: 28 Feb 2024
Posts: 1,101
Own Kudos:
1,365
 [1]
Given Kudos: 351
Location: India
Posts: 1,101
Kudos: 1,365
 [1]
If DA = DB, CD = CB and AB = AC, then x= 09 Jul 2021, 10:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
As, 180-p = 180- 2x or, p = 2x

So, x+ (x+2x) + (x+2x) = 180 or, x = 180/7.

I think A. :)
User avatar
bansalgaurav
User avatar
Joined: 26 Mar 2021
Last visit: 20 Nov 2021
Posts: 112
Own Kudos:
32
 [2]
Given Kudos: 36
Location: India
Concentration: General Management, Strategy
Schools: IIMB EPGP'23
GMAT 1: 640 Q50 V25
Schools: IIMB EPGP'23
GMAT 1: 640 Q50 V25
Posts: 112
Kudos: 32
 [2]
If DA = DB, CD = CB and AB = AC, then x= 09 Jul 2021, 11:58
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
this Q. is an application of the following two theorems:
1: Angles opposite to equal sides in a triangle are equal.
2: Exterior angle is equal to the sum of interior opposite angles


I hope the rest is easy to solve !!!! check the solution image uploaded by zanto.
User avatar
HarshaBujji
User avatar
Joined: 29 Jun 2020
Last visit: 11 Sep 2026
Posts: 731
Own Kudos:
941
 [1]
Given Kudos: 248
Location: India
Products:
My Reviews Forum Quiz
Posts: 731
Kudos: 941
 [1]
If DA = DB, CD = CB and AB = AC, then x= 10 Jul 2021, 06:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO A,

Post making all the angles in ABC interms of x , We know sum of angles is 180

Hence x is 180/7.

Posted from my mobile device
Attachments

IMG_20210710_184821.jpg
IMG_20210710_184821.jpg [ 62.37 KiB | Viewed 2996 times ]

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,229
Own Kudos:
1,159
Posts: 39,229
Kudos: 1,159
If DA = DB, CD = CB and AB = AC, then x= 17 Mar 2023, 03:55
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
113520 posts