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# In pentagon ABCDE above, x =

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Math Expert
Joined: 02 Sep 2009
Posts: 55639
In pentagon ABCDE above, x =  [#permalink]

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11 Jan 2019, 02:17
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:20) correct 14% (01:45) wrong based on 27 sessions

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In pentagon ABCDE above, x =

A. 65
B. 75
C. 80
D. 105
E. 115

Attachment:

2019-01-11_1315.png [ 15.31 KiB | Viewed 447 times ]

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Joined: 14 Jul 2013
Posts: 16
Re: In pentagon ABCDE above, x =  [#permalink]

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11 Jan 2019, 05:02
Sum of the interior angles of a pentagon = 18(n-2); where n=5 > 180(3) = 540

x = (540 - (180+130))/2 = 115

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CEO
Joined: 18 Aug 2017
Posts: 3866
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: In pentagon ABCDE above, x =  [#permalink]

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11 Jan 2019, 05:12
Bunuel wrote:

In pentagon ABCDE above, x =

A. 65
B. 75
C. 80
D. 105
E. 115

Attachment:
2019-01-11_1315.png

sum of internal angle of pentagon = (n-2) * 180 = 3 * 180 = 540
sum ; 2x+130+180 = 540
x= 115
IMO E
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Manager
Joined: 18 Oct 2018
Posts: 83
Location: India
GPA: 4
Re: In pentagon ABCDE above, x =  [#permalink]

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11 Jan 2019, 11:41
Sum of angles in a polygon of n sides= (n-2)*180
Here, pentagon has n=5
So, 90+90+130+x+x=(5-2)*180=540
Hence, x=115
Re: In pentagon ABCDE above, x =   [#permalink] 11 Jan 2019, 11:41
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