Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Feb 2013
Posts: 916
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
Updated on: 02 Nov 2014, 08:22
1
This post received KUDOS
10
This post was BOOKMARKED
Question Stats:
55% (01:47) correct 45% (01:45) wrong based on 155 sessions
HideShow timer Statistics
Attachment: File comment: Economist.png
Economist.png [ 19.8 KiB  Viewed 3055 times ]
If a circle is circumscribed around a regular pentagon, as shown above, what is the value of x? A) 72 B) 108 C) 135 D) 140 E) 144
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful
Originally posted by kinjiGC on 02 Nov 2014, 08:18.
Last edited by Bunuel on 02 Nov 2014, 08:22, edited 2 times in total.
Renamed the topic and edited the question.





Director
Joined: 03 Feb 2013
Posts: 916
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
02 Nov 2014, 08:21
2
This post received KUDOS
Each side subtends an angle of 360/5 = 72 at the center. Then the angle of EBD = 72/2 = 36 lets assume the point where X is specified is named as F So EBDF becomes a cyclic quadrilateral. Hence Angle EBD and Angle EFD should be supplementary and hence X = 180  36 = 144.
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



Manager
Joined: 30 Mar 2013
Posts: 113

If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
Updated on: 03 Nov 2014, 03:34
kinjiGC wrote: Each side subtends an angle of 360/5 = 72 at the center. Then the angle of EBD = 72/2 = 36 lets assume the point where X is specified is named as F So EBDF becomes a cyclic quadrilateral.
Hence Angle EBD and Angle EFD should be supplementary and hence X = 180  36 = 144. EDIT: this is the property of any cyclic quad (and not a kite), just looked it up. thanks!
Originally posted by usre123 on 03 Nov 2014, 01:26.
Last edited by usre123 on 03 Nov 2014, 03:34, edited 1 time in total.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
03 Nov 2014, 01:30
kinjiGC wrote: Each side subtends an angle of 360/5 = 72 at the center. Then the angle of EBD = 72/2 = 36 lets assume the point where X is specified is named as F So EBDF becomes a cyclic quadrilateral.
Hence Angle EBD and Angle EFD should be supplementary and hence X = 180  36 = 144. Is EF = FD mentioned in the problem (or we have to assume from the diagram)?
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Joined: 30 Mar 2013
Posts: 113

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
03 Nov 2014, 01:41
^ same question i was about to ask as well



Director
Joined: 03 Feb 2013
Posts: 916
Location: India
Concentration: Operations, Strategy
GPA: 3.88
WE: Engineering (Computer Software)

If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
03 Nov 2014, 05:57
PareshGmat wrote: kinjiGC wrote: Each side subtends an angle of 360/5 = 72 at the center. Then the angle of EBD = 72/2 = 36 lets assume the point where X is specified is named as F So EBDF becomes a cyclic quadrilateral.
Hence Angle EBD and Angle EFD should be supplementary and hence X = 180  36 = 144. Is EF = FD mentioned in the problem (or we have to assume from the diagram)? usre123 wrote: ^ same question i was about to ask as well EF = FD is not required as chord will subtend the same angle in an arc whatever may be the point on the circle. Circle properties For example Angle EBD = Angle EAD = Angle ECD etc. Similarly below the chord as well.
_________________
Thanks, Kinjal My Debrief : http://gmatclub.com/forum/hardworknevergetsunrewardedforever189267.html#p1449379 My Application Experience : http://gmatclub.com/forum/hardworknevergetsunrewardedforever18926740.html#p1516961 Linkedin : https://www.linkedin.com/in/kinjaldas/
Please click on Kudos, if you think the post is helpful



Intern
Joined: 04 Jul 2014
Posts: 46

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
20 Dec 2014, 04:05
kinjiGC wrote: Attachment: Economist.png If a circle is circumscribed around a regular pentagon, as shown above, what is the value of x? A) 72 B) 108 C) 135 D) 140 E) 144 360 * 4/5 = 72 * 4 [72*4] / 2 = 36 * 4 = 144 Ans E.



Intern
Joined: 04 Jul 2014
Posts: 46

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
20 Dec 2014, 09:14
kinjiGC wrote: Attachment: Economist.png If a circle is circumscribed around a regular pentagon, as shown above, what is the value of x? A) 72 B) 108 C) 135 D) 140 E) 144 360 * 4/5 = 72 * 4 [72*4] / 2 = 36 * 4 = 144 Ans E.



Current Student
Status: Applied
Joined: 02 May 2014
Posts: 157
Location: India
Concentration: Operations, General Management
Schools: Tulane '18 (A), Tippie '18 (D), Moore '18, Katz '18 (D), UCSD '18, Madison '18, Olin '18 (S), Simon '18, Desautels '18 (I), Sauder '18 (S), Terry '18 (WL), GWU '18, Neeley '18 (WL), Weatherhead '18 (S), Fox(Temple)'18, Eller FT'18 (A), Schulich Sept"18 (S)
GPA: 3.35
WE: Information Technology (Computer Software)

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
12 Jan 2015, 02:14
1
This post received KUDOS
1
This post was BOOKMARKED
Each arc is equal to 360/5=72 since it is a regular pentagon. Now the major arch ED is equal to 36072=288 so angle substended by it at the circumferance 288/2=144.



Director
Joined: 07 Dec 2014
Posts: 967

If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
09 Jul 2016, 15:31
look at x as an interior angle of a regular decagon (102)(180°)=1440° total interior degrees 1440°/10=144° interior angle degrees



Intern
Joined: 02 Jul 2016
Posts: 3

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
10 Jul 2016, 02:38
Hi guys,
I'm new here and this is my first post on the forum. Really struggling to get my head around this question and understand how it works. Would really appreciate if someone could show a clear step by step process of how they got the answer.
Thanks



Intern
Joined: 12 Jun 2016
Posts: 27
Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.76
WE: Information Technology (Computer Software)

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
31 Jul 2016, 00:32
1
This post received KUDOS
Angle subtend by the arc ED at the center = 360/5 = 72.
As per the property of the circle: Angle subtended by an arc at any point on the circumference of a circle is 1/2 times the angle subtended by the same arc on the center.
Hence, angle EBD = (1/2)*72 = 36. Now, Points E,B,D and the point where angle x is forming, makes a cyclic quadrilateral. So, angle EBD + x = 180 x = 180  36 = 144. Ans. E



Intern
Joined: 02 Jul 2016
Posts: 3

Re: If a circle is circumscribed around a regular pentagon, as shown above [#permalink]
Show Tags
31 Jul 2016, 17:34
Thanks shashank1tripathi really helpful reply! Got it now!




Re: If a circle is circumscribed around a regular pentagon, as shown above
[#permalink]
31 Jul 2016, 17:34






