Last visit was: 18 Sep 2026, 01:20 It is currently 18 Sep 2026, 01:20
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
655-705 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Sep 2026
Posts: 113,643
Own Kudos:
841,971
 [8]
Given Kudos: 111,635
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,643
Kudos: 841,971
 [8]
What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 09:45
1
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

53% (02:14) correct 47% (02:26) wrong based on 64 sessions

History

Date
Time
Result
Not Attempted Yet

What is the measure of an angle marked with ? of a regular seven-point star shown above?

A. 90/7
B. 120/7
C. 180/7
D. 240/7
E. 540/7

Show Spoiler
Find an angle of a regular seven-point star.
Attachment:
Untitled.png
Untitled.png [ 6.99 KiB | Viewed 9038 times ]
ShowHide Answer
Official Answer
E
avatar
sahuayush
avatar
Joined: 02 Apr 2020
Last visit: 15 Sep 2026
Posts: 18
Own Kudos:
24
 [1]
Given Kudos: 271
Posts: 18
Kudos: 24
 [1]
What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 10:14
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel, are the options provided correct?

My answer is coming to 540/7, for the angle at the vertex of the star.

Posted from my mobile device
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,877
Own Kudos:
5,544
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,877
Kudos: 5,544
What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 11:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sahuayush
Bunuel, are the options provided correct?

My answer is coming to 540/7, for the angle at the vertex of the star.

Posted from my mobile device
Show more
IMHO (C) 180/7
avatar
sahuayush
avatar
Joined: 02 Apr 2020
Last visit: 15 Sep 2026
Posts: 18
Own Kudos:
24
Given Kudos: 271
Posts: 18
Kudos: 24
What is the measure of an angle of a regular seven-point star? Updated on: 12 Dec 2020, 04:17
Originally posted by sahuayush on 04 Dec 2020, 11:42.
Last edited by sahuayush on 12 Dec 2020, 04:17, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
.
User avatar
stony
User avatar
Joined: 12 Nov 2017
Last visit: 19 Sep 2022
Posts: 2
Own Kudos:
2
 [1]
Given Kudos: 12
Posts: 2
Kudos: 2
 [1]
What is the measure of an angle of a regular seven-point star? 04 Dec 2020, 16:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The central angle is 360/7 so it has to be 540/7.

Posted from my mobile device
avatar
sahuayush
avatar
Joined: 02 Apr 2020
Last visit: 15 Sep 2026
Posts: 18
Own Kudos:
24
Given Kudos: 271
Posts: 18
Kudos: 24
What is the measure of an angle of a regular seven-point star? 11 Dec 2020, 20:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel, can you post how you arrived at the solution?

Posted from my mobile device
avatar
sahuayush
avatar
Joined: 02 Apr 2020
Last visit: 15 Sep 2026
Posts: 18
Own Kudos:
24
Given Kudos: 271
Posts: 18
Kudos: 24
What is the measure of an angle of a regular seven-point star? 12 Dec 2020, 04:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@chetan2u can you share the explanation?

Posted from my mobile device
User avatar
Hea234ven
User avatar
Joined: 12 Jul 2019
Last visit: 20 Sep 2021
Posts: 58
Own Kudos:
46
Given Kudos: 678
Status:No knowledge goes waste
Location: Norway
Concentration: Finance, Economics
GPA: 3.3
WE:Corporate Finance (Commercial Banking)
Posts: 58
Kudos: 46
What is the measure of an angle of a regular seven-point star? 15 Dec 2020, 21:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I need answer explanation.
avatar
ayerhs
avatar
Joined: 30 May 2020
Last visit: 26 Feb 2021
Posts: 17
Own Kudos:
7
Given Kudos: 309
Posts: 17
Kudos: 7
What is the measure of an angle of a regular seven-point star? 20 Dec 2020, 22:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CrackVerbalGMAT can you help with solution here?
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 14 Sep 2026
Posts: 4,849
Own Kudos:
9,373
 [3]
Given Kudos: 230
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,849
Kudos: 9,373
 [3]
What is the measure of an angle of a regular seven-point star? 21 Dec 2020, 02:39
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Hi Bunuel, the answer which I'm getting is 540/7.


Please refer to the diagram below. A regular star polygon should be like this.


There are 7 equal arcs on the circle. arc AB = arc BC = arc CD = arc DE = arc EF = arc FG = arc GA


\(\angle{\alpha} = \frac{1}{2} * arc \space FEDC\)


Arc FEDC = arc FE + arc EB + arc BC = 3/7 th of the circle = 3/7 * 360 = 1080/7

Therefore \(\alpha = \frac{1}{2} * \frac{1080}{7} = \frac{540}{7}\)

Option E

Arun Kumar
Attachments

Heptagon.jpg
Heptagon.jpg [ 668.53 KiB | Viewed 7516 times ]

User avatar
Hea234ven
User avatar
Joined: 12 Jul 2019
Last visit: 20 Sep 2021
Posts: 58
Own Kudos:
46
Given Kudos: 678
Status:No knowledge goes waste
Location: Norway
Concentration: Finance, Economics
GPA: 3.3
WE:Corporate Finance (Commercial Banking)
Posts: 58
Kudos: 46
What is the measure of an angle of a regular seven-point star? 21 Dec 2020, 07:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CrackVerbalGMAT
Hi Bunuel, the answer which I'm getting is 540/7.


Please refer to the diagram below. A regular star polygon should be like this.


There are 7 equal arcs on the circle. arc AB = arc BC = arc CD = arc DE = arc EF = arc FG = arc GA


\(\angle{\alpha} = \frac{1}{2} * arc \space FEDC\)


Arc FEDC = arc FE + arc EB + arc BC = 3/7 th of the circle = 3/7 * 360 = 1080/7

Therefore \(\alpha = \frac{1}{2} * \frac{1080}{7} = \frac{540}{7}\)

Option E

Arun Kumar
Show more

How did u come to- angle a= 1/2 * arc fedc? Is there any formulae?

Posted from my mobile device
avatar
ayerhs
avatar
Joined: 30 May 2020
Last visit: 26 Feb 2021
Posts: 17
Own Kudos:
7
 [1]
Given Kudos: 309
Posts: 17
Kudos: 7
 [1]
What is the measure of an angle of a regular seven-point star? 21 Dec 2020, 07:58
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hea234ven

Angle subtended by an arc/chord at the center is double of the angle subtended by the same arc/chord at the circumference.
Sorry can't post picture. You can google it.
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 14 Sep 2026
Posts: 4,849
Own Kudos:
9,373
Given Kudos: 230
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,849
Kudos: 9,373
What is the measure of an angle of a regular seven-point star? 22 Dec 2020, 05:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hea234ven


How did u come to- angle a= 1/2 * arc fedc? Is there any formulae?

Posted from my mobile device
Show more


There are a couple of equations based on the arc angle.

The simplest is that the arc angle is equal to the central angle subtended by the ends of the arc at the center.

Now this gets related to the property of the chord, where the the angle subtended by the chord at the center, is twice the angle subtended by the same chord at the circumference.

Based on this, the arc angle is twice the angle made by the ends of the arc at the circumference.


Hope this helps

Arun Kumar
Attachments

arc angles.jpg
arc angles.jpg [ 362.29 KiB | Viewed 7282 times ]

Moderator:
Bunuel
Math Expert
113643 posts