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

Question

https://gmatclub.com/forum/download/file.php?id=25984 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 . originals.jpg

Lucky2783 · Answer

uploaded the image with the solution . 
answer A.

peachfuzz · Answer

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

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: originals (1).jpg 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 originals (2).jpg 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)

ShanDhar · Answer

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

bumpbot · Answer

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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?

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