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# In the circle above with center O, x + y =

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Math Expert
Joined: 02 Sep 2009
Posts: 47001
In the circle above with center O, x + y = [#permalink]

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21 Nov 2017, 23:32
00:00

Difficulty:

25% (medium)

Question Stats:

89% (00:39) correct 11% (01:36) wrong based on 36 sessions

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In the circle above with center O, x + y =

(A) 110
(B) 125
(C) 180
(D) 240
(E) 250

Attachment:

2017-11-22_1023.png [ 8.49 KiB | Viewed 461 times ]

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Intern
Joined: 29 Aug 2016
Posts: 33
Re: In the circle above with center O, x + y = [#permalink]

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22 Nov 2017, 00:14
1

The sum of interior angles of any given Triangle is 180. Also, both these triangles are Isosceles because 2 sides of these triangles are equal (radius).

Y is therefore 60.
X is 50.
X+Y is 110.

Hence A.

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Manager
Joined: 20 Feb 2017
Posts: 119
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Re: In the circle above with center O, x + y = [#permalink]

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22 Nov 2017, 04:07
simple question
65+65+x= 180
=> x = 50
60+60+y = 180
y= 60
x+y = 110
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Joined: 04 Mar 2011
Posts: 2669
Re: In the circle above with center O, x + y = [#permalink]

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27 Nov 2017, 12:32
Bunuel wrote:

In the circle above with center O, x + y =

(A) 110
(B) 125
(C) 180
(D) 240
(E) 250

Attachment:
2017-11-22_1023.png

Each triangle has two legs emanating from the center O, each of which is a radius of the circle.

We see that the top triangle is an isosceles triangle with two 65-degree angles . Thus x = 180 - 65 - 65 = 50.

We see that the bottom triangle is also an isosceles triangle with two 60-degree angles. Thus y = 180 - 60 - 60 = 60.

So x + y = 50 + 60 = 110.

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Re: In the circle above with center O, x + y =   [#permalink] 27 Nov 2017, 12:32
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