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

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

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New post 20 Nov 2017, 23:16
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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

[Reveal] Spoiler:
Attachment:
2017-11-21_1004.png
2017-11-21_1004.png [ 8.99 KiB | Viewed 511 times ]
[Reveal] Spoiler: OA

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

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New post 20 Nov 2017, 23:57
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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New post 21 Nov 2017, 00:15
x+y=360-2*135=90
Answer C

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

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New post 21 Nov 2017, 00:29
Attachment:
2017-11-21_1004.png
2017-11-21_1004.png [ 9.87 KiB | Viewed 320 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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New post 21 Nov 2017, 08:34
Bunuel wrote:
Image
If C is the center of the circle above, then x + y =

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

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

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New post 21 Nov 2017, 09:04
Bunuel wrote:
Image
If C is the center of the circle above, then x + y =

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

[Reveal] Spoiler:
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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New post 21 Nov 2017, 10:03
1
This post received
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Expert's post
chetan2u wrote:
Bunuel wrote:
Image
If C is the center of the circle above, then x + y =

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

[Reveal] Spoiler:
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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New to the Math Forum?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 27 Nov 2017, 11:50
Bunuel wrote:
Image
If C is the center of the circle above, then x + y =

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

[Reveal] Spoiler:
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.

Answer: C
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Kudos [?]: 979 [0], given: 5

Re: If C is the center of the circle above, then x + y =   [#permalink] 27 Nov 2017, 11:50
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