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# If C is the center of the circle above, then x + y =

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
If C is the center of the circle above, then x + y =  [#permalink]

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20 Nov 2017, 22:16
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Difficulty:

5% (low)

Question Stats:

92% (00:28) correct 8% (00:14) wrong based on 80 sessions

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If C is the center of the circle above, then x + y =

(A) 45
(B) 65
(C) 90
(D) 100
(E) 130

Attachment:

2017-11-21_1004.png [ 8.99 KiB | Viewed 813 times ]

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Re: If C is the center of the circle above, then x + y =  [#permalink]

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20 Nov 2017, 22:57
The answer is C. 90 degrees.

X and Y are vertically opposite angles.
Also, C is the centre and hence the angle subtended by the arc must be 180 degrees.
135 and x are supplementary. Similarly 135 and y too.

We can conclude from there that x=y= 45 degrees. So the sum is 90.

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Re: If C is the center of the circle above, then x + y =  [#permalink]

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20 Nov 2017, 23:15
x+y=360-2*135=90
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Re: If C is the center of the circle above, then x + y =  [#permalink]

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20 Nov 2017, 23:29
Attachment:

2017-11-21_1004.png [ 9.87 KiB | Viewed 617 times ]

From the figure, in line AB, the sum of angles is 180, which makes angle x = 180 - 135 = 45
Similarly, the sum of angles in line XY is also 180, making angle y = 45

We can also say that y=45 because x and y are vertically opposite angles.

Hence, x+y = 90(Option C)
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Re: If C is the center of the circle above, then x + y =  [#permalink]

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21 Nov 2017, 07:34
Bunuel wrote:

If C is the center of the circle above, then x + y =

(A) 45
(B) 65
(C) 90
(D) 100
(E) 130

Attachment:
2017-11-21_1004.png

135+y = 180

So, y = 45

Further x = y = 45

Hence, x + y = 90 , answer will be (C)
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Posts: 7035
Re: If C is the center of the circle above, then x + y =  [#permalink]

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21 Nov 2017, 08:04
Bunuel wrote:

If C is the center of the circle above, then x + y =

(A) 45
(B) 65
(C) 90
(D) 100
(E) 130

Attachment:
2017-11-21_1004.png

Hi..
Bunuel, may be specifying that the two lines are straight lines would clarify the question a bit more, otherwise it could be just four radius drawn from center
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Re: If C is the center of the circle above, then x + y =  [#permalink]

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21 Nov 2017, 09:03
1
chetan2u wrote:
Bunuel wrote:

If C is the center of the circle above, then x + y =

(A) 45
(B) 65
(C) 90
(D) 100
(E) 130

Attachment:
2017-11-21_1004.png

Hi..
Bunuel, may be specifying that the two lines are straight lines would clarify the question a bit more, otherwise it could be just four radius drawn from center

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Re: If C is the center of the circle above, then x + y =  [#permalink]

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27 Nov 2017, 10:50
Bunuel wrote:

If C is the center of the circle above, then x + y =

(A) 45
(B) 65
(C) 90
(D) 100
(E) 130

Attachment:
2017-11-21_1004.png

A circle contains 360 degrees, and a semicircle contains 180 degrees. We see that both 135 + x = 180 and 135 + y = 180, so both x and y are 45; thus, x + y = 90.

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Re: If C is the center of the circle above, then x + y = &nbs [#permalink] 27 Nov 2017, 10:50
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