Last visit was: 27 Apr 2026, 10:05 It is currently 27 Apr 2026, 10:05
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
ratan19
User avatar
Joined: 30 Jul 2010
Last visit: 16 Jun 2013
Posts: 2
Own Kudos:
8
 [3]
Given Kudos: 3
Location: India
GMAT Date: 04-14-2013
Posts: 2
Kudos: 8
 [3]
The ratio of the adjacent angles of a parallelogram is 7 : 8 Updated on: 14 Mar 2013, 06:18
Originally posted by ratan19 on 14 Mar 2013, 05:18.
Last edited by Bunuel on 14 Mar 2013, 06:18, edited 1 time in total.
Renamed the topic and edited the question.
Kudos
Add Kudos
3
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:

63% (01:52) correct 37% (01:57) wrong based on 167 sessions

History

Date
Time
Result
Not Attempted Yet
The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?

(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
ShowHide Answer
Official Answer
A
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,579
 [2]
Given Kudos: 105,914
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,928
Kudos: 811,579
 [2]
The ratio of the adjacent angles of a parallelogram is 7 : 8 14 Mar 2013, 06:27
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ratan19
The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?

(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
Show more

The adjacent angles of a parallelogram are supplementary (supplementary angles are two angles that add up to 180°), so we have that 7x+8x=180° --> x=12 --> the smaller angle of the parallelogram is 7x=84°.

Next, the sum of interior angles of a polygon is 180(n-2) where n is the number of sides (so is the number of angles). So, the sum of the interior angles of any quadrilateral is 180*2=360°. So, we have that 5y+6y+7y+12y=360° --> y=12° --> the second largest angle of the quadrilateral is 7y=84°.

The sum = 84°+84°=168°.

Answer: A.

For more on polygons check Polygons chapter of Math Book: math-polygons-87336.html

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.
User avatar
ratan19
User avatar
Joined: 30 Jul 2010
Last visit: 16 Jun 2013
Posts: 2
Own Kudos:
8
Given Kudos: 3
Location: India
GMAT Date: 04-14-2013
Posts: 2
Kudos: 8
The ratio of the adjacent angles of a parallelogram is 7 : 8 14 Mar 2013, 06:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thank you very much, Bunuel!
User avatar
HarveyS
User avatar
Joined: 14 Jan 2013
Last visit: 25 Apr 2017
Posts: 112
Own Kudos:
1,765
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Posts: 112
Kudos: 1,765
The ratio of the adjacent angles of a parallelogram is 7 : 8 11 Apr 2013, 06:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Pls suggest , why we haven't added 5 y ( 5 *12) + 7 y ( 7*12) = 144...
User avatar
Zarrolou
User avatar
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 842
Own Kudos:
5,188
Given Kudos: 219
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 842
Kudos: 5,188
The ratio of the adjacent angles of a parallelogram is 7 : 8 11 Apr 2013, 06:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
targetbschool
Pls suggest , why we haven't added 5 y ( 5 *12) + 7 y ( 7*12) = 144...
Show more

Read the question carefully:
"What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?"
smaller angle of the parallelogram=7*12°=84°.
second largest angle of the quadrilateral=7*12°=84°.
84°+84°=168°
User avatar
HarveyS
User avatar
Joined: 14 Jan 2013
Last visit: 25 Apr 2017
Posts: 112
Own Kudos:
1,765
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Posts: 112
Kudos: 1,765
The ratio of the adjacent angles of a parallelogram is 7 : 8 11 Apr 2013, 06:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
oops... My bad :( ...

Thanks for prompt reply..
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,902
Own Kudos:
5,457
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,902
Kudos: 5,457
The ratio of the adjacent angles of a parallelogram is 7 : 8 10 May 2016, 09:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ratan19
The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?

(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
Show more

The measures of the adjacent angles of a parallelogram add up to be 180°

Given

Quote:
The ratio of the adjacent angles of a parallelogram is 7 : 8
Show more

So, 7x + 8x = 180°

Or, 15x = 180°

Or, x = 12°

Hence the angles of the parallelogram are 84° and 96°

Further it is given

Quote:
ratio of the angles of quadrilateral is 5 : 6 : 7 : 12
Show more

We know sum of all the four angles of a quadrilateral is 360°

So, 5y + 6y + 7y + 12 y = 360°

Or, 5y + 6y + 7y + 12 y = 360°

Or, 30y = 360°

Or, y = 12°

Hence the angles of the quadrilateral are 60° , 72, 84° and 144°

Quote:
sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral
Show more

Will be 84° + 84° = 168°

Hence correct answer will be (A) 168° :-D :P
User avatar
Divyadisha
User avatar
Current Student
Joined: 18 Oct 2014
Last visit: 01 Jun 2018
Posts: 660
Own Kudos:
1,958
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT 1: 660 Q49 V31
Posts: 660
Kudos: 1,958
The ratio of the adjacent angles of a parallelogram is 7 : 8 10 May 2016, 11:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sum of adjacent angles of parallelogram is 180
7x+8x= 180
x= 12
Smallest angle = 12*7------1

Sum of all angles of a Quadrilateral is 360
5y+6y+7y+12y= 360
y=12
2nd largest angle= 7*12-----2

Sum of equation 1 and 2
2*12*7= 168

'A' is the answer
User avatar
rhine29388
User avatar
Joined: 24 Nov 2015
Last visit: 21 Oct 2019
Posts: 386
Own Kudos:
146
Given Kudos: 231
Location: United States (LA)
Products:
My Reviews
Posts: 386
Kudos: 146
The ratio of the adjacent angles of a parallelogram is 7 : 8 06 Jun 2016, 13:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Adjacent angles of a parallelogram are supplementary (their total is \(180^{\circ}\))
consider common ratio for angles of parallelogram as x
7x + 8x = 180
15x = 180
x = 12
so smaller of the 2 angles is 7x = 7 * 12 =\(84^{\circ}\)

sum of all angles of a quadrilateral is \(360^{\circ}\)
consider common ratio for angles of quadrilateral as y
5y + 6y + 7y + 12y = 360
30y = 360
y = 12
second largest angle of the quadrilateral is 7x = 7 * 12 =\(84^{\circ}\)

sum of smaller of the 2 angles of parallelogram and second largest angle of the quadrilateral is 84 +84 = \(168^{\circ}\)
Correct Answer - A
User avatar
brs1cob
User avatar
Joined: 06 Jun 2013
Last visit: 11 Apr 2020
Posts: 116
Own Kudos:
39
Given Kudos: 339
Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE:Engineering (Computer Software)
Schools: Tuck
GMAT 1: 640 Q49 V30
Posts: 116
Kudos: 39
The ratio of the adjacent angles of a parallelogram is 7 : 8 02 Jul 2017, 00:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
only thing we need to keep in mind is the question is talking about two entities: parallelogram n quadrilateral. once this is clear, we can easily find out all the angles.

answer is A
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,119
Posts: 38,986
Kudos: 1,119
The ratio of the adjacent angles of a parallelogram is 7 : 8 05 Nov 2024, 16:01
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.
Moderators:
Bunuel
Math Expert
109928 posts
Krunaal
Tuck School Moderator
852 posts