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What is the value of w in terms of x and y?

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What is the value of w in terms of x and y?  [#permalink]

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New post 19 Mar 2015, 06:07
1
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (02:27) correct 32% (02:10) wrong based on 112 sessions

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Re: What is the value of w in terms of x and y?  [#permalink]

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New post 19 Mar 2015, 06:21
Bunuel wrote:
Attachment:
The attachment originals.jpg is no longer available
What is the value of w in terms of x and y? Note: Figure not drawn to scale

A. 2x + 2y - 180
B. 180 - x - y
C. 360 - 2x - 2y
D. 360 - 2x - 3y
E. 180 + x - 2y

Kudos for a correct solution.



uploaded the image with the solution .
answer A.
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Re: What is the value of w in terms of x and y?  [#permalink]

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New post 19 Mar 2015, 06:46
The angles of a triangle sums up to 180. A straight line is 180.

the smaller triangle that holds angle w has angles of w, 180-x-y, and 180-x-y.

180 = w + 180-x-y + 180-x-y
w = 2x+2y-180

Answer: A
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Re: What is the value of w in terms of x and y?  [#permalink]

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New post 19 Mar 2015, 20:26
1
Hi All,

For anyone who finds this question 'complex-looking', you can solve it rather easily by TESTing VALUES. There are a few math rules that you have to follow though:

1) The angles in a line sum to 180 degrees
2) The angles in a triangle sum to 180 degrees

Try TESTing a VALUE for X and Y, then fill in all of the various angles in this picture.....You'll end up with a value for W and a way to see if the various answers match.

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Re: What is the value of w in terms of x and y?  [#permalink]

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New post 23 Mar 2015, 04:54
Bunuel wrote:
Image
What is the value of w in terms of x and y? Note: Figure not drawn to scale

A. 2x + 2y - 180
B. 180 - x - y
C. 360 - 2x - 2y
D. 360 - 2x - 3y
E. 180 + x - 2y

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
originals (1).jpg
originals (1).jpg [ 20.79 KiB | Viewed 5495 times ]

Here's the same diagram with letters. First of all, look at the big triangle, triangle ACE. We know the three angles in this or any triangle must add up to 180°. Let's say that ∠E = k. Then we know

x + y + k = 180, or k = 180 – x – y

Now, look at the angles around point F. Those three angles form a straight line, that is to say, a 180° angle, so the sum of the three angles there must also be 180°. Since one is x and one is y, the other has to be k --- ∠DFE = k
Attachment:
originals (2).jpg
originals (2).jpg [ 21.54 KiB | Viewed 5491 times ]


Now, look at triangle DEF. The sum of the three angles in this triangle must also be 180°.

w + k + k = 180°

w = 180 – 2k

Now, we have an expression for w in terms of k. To express w in terms of x & y, we need to substitute the expression for k above, k = 180 – x – y

w = 180 – 2(180 – x – y)

w = 180 – 360 + 2x + 2y

w = 2x + 2y – 180

Answer = (A)
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Re: What is the value of w in terms of x and y?  [#permalink]

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New post 08 Jul 2019, 01:13
Here
w+x+y = 180 degree -----------------------------1
so <x = 180 degree - x -y
and <y = 180 degree - x -y
then put the value of angle x and y in equation 1
w+ 180 degree - x -y +180 degree - x -y = 180 degree
w+360 degree - 2x-2y = 180 degree
w = 2x + 2y -360 degree +180 degree
w = 2x+2y -180
The result abjectly matches with A
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Re: What is the value of w in terms of x and y?   [#permalink] 08 Jul 2019, 01:13
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