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# If BD = CD, what is the degree measure of x + y?

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Math Expert
Joined: 02 Sep 2009
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If BD = CD, what is the degree measure of x + y?  [#permalink]

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01 Apr 2016, 04:18
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79% (01:08) correct 21% (01:31) wrong based on 171 sessions

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If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

Attachment:

touchingtriangles.jpg [ 3.4 KiB | Viewed 2362 times ]

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Re: If BD = CD, what is the degree measure of x + y?  [#permalink]

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01 Apr 2016, 04:47
Okay here is my approach
we need to get x+y
as per statement 1 => u = given so as u=v => we have v too
great..
now using angle sum property => we have w too
now using the exterior angle property => z=w+u => we have z too
again using angle sum property we have x+y too
hence sufficient.
similarly we have statement 2 => sufficient
hence D
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Re: If BD = CD, what is the degree measure of x + y?  [#permalink]

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03 Apr 2016, 04:21
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

When you modify the original condition and the question, x+y=v is derived. From, v=u and w+2v=180, if you figure out w, you can figure out v as well.
For 1), v=74 and it is sufficient.
For 2), substitute w=32 to w+2v=180 -> 32+2v=180, 2v=148 and v=74.
Thus, 1)=2) and the answer is D.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If BD = CD, what is the degree measure of x + y?  [#permalink]

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18 Sep 2016, 00:03
Bunuel wrote:

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

Attachment:
touchingtriangles.jpg

For such questions..is it not necessary to have "Ac is straight line "mentioned in stem itself???

Thanks
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Re: If BD = CD, what is the degree measure of x + y?  [#permalink]

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18 Sep 2016, 01:10
rohit8865 wrote:
Bunuel wrote:

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

Attachment:
touchingtriangles.jpg

For such questions..is it not necessary to have "Ac is straight line "mentioned in stem itself???

Thanks

Unless we are explicitly stated that the figure is not drawn to scale, we should take the given figure as it appears.
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Re: If BD = CD, what is the degree measure of x + y?  [#permalink]

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29 May 2017, 10:01
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Bunuel wrote:

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

Attachment:
touchingtriangles.jpg

This problem is all about preparation. Once you re-draw the triangle, you will note that x+y = v since an exterior angle of a triangle is equal to the sum of the opposite interior angles. Likewise, u = v since BC = CD. So we really need to determine either the value of v or u or even the value of w.

Statement 1) v = 74. Sufficient.

Statement 2) w = 32.

w = 32
v+u + 32 = 180
2v + 32 = 180 since v=u
2v = 148
v = 74

Sufficient.
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Re: If BD = CD, what is the degree measure of x + y?  [#permalink]

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06 Sep 2017, 19:15
Bunuel wrote:

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

Attachment:
touchingtriangles.jpg

An interesting thing about this question is that if know how similar triangles work, then we can basically see that statement 1 and statement 2 have the exact same usefulness as each other- from statement 1 we can derive the exact same amount of information as statement 2 and vice-versa.

D
Re: If BD = CD, what is the degree measure of x + y?   [#permalink] 06 Sep 2017, 19:15
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