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In the figure above, what is the value of 2x - y?

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In the figure above, what is the value of 2x - y?  [#permalink]

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New post 25 Nov 2018, 09:54
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A
B
C
D
E

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Question Stats:

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In the figure above, what is the value of 2x - y?

(A) 0
(B) 15
(C) 30
(D) 45
(E) 60

Project PS Butler : Question #39


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Attachment:
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Angles.JPG [ 15.28 KiB | Viewed 1075 times ]

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Re: In the figure above, what is the value of 2x - y?  [#permalink]

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New post 25 Nov 2018, 10:05
1
x = 45 - 30 = 15, since the right triangle formed has angles 90, 45 and (x+30) which is equal to 45
y = 60 - 45 = 15, since the other right triangle formed has angles 90, 30 and (x + 45) which is equal to 60

2x - y = 2*15 - 15 = 15

Hence Option B
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Re: In the figure above, what is the value of 2x - y?  [#permalink]

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New post 26 Nov 2018, 10:52
Triangle A --> (x+30) + 45 =90
x=15
Triangle B --> (y+45) + 30 =90
y=15
2(15)-15= 15
B
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Re: In the figure above, what is the value of 2x - y?  [#permalink]

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New post 02 Dec 2018, 10:40
Top Contributor
HKD1710 wrote:
Image
In the figure above, what is the value of 2x - y?

(A) 0
(B) 15
(C) 30
(D) 45
(E) 60

Project PS Butler : Question #39


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Attachment:
Angles.JPG


Here's a different approach:

Since angles in a triangle must add to 180°, the 3rd angle in the blue triangle must be 105°
Image

Since angles on a line must add to 180°, we know the two angles below are each75°
Image

Finally, since angles in a triangle must add to 180° . . .
Image
. . . we can see that x = 15° and y = 15°

What is the value of 2x - y?
2x - y = 2(15°) - 15° = 30° - 15° = 15°

Answer: B

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Re: In the figure above, what is the value of 2x - y?   [#permalink] 02 Dec 2018, 10:40
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