Triangle question

[pinal2]

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

(1) v = 74 degrees

(2) w = 32 degrees




The answer is "EACH statement ALONE is sufficient.". The explanation given is pasted below

The question asks us to find the number of degrees in x + y. Since the sum of the angles in any triangle is 180 degrees, we know that x + y + z = 180, so if we can find z we can find x + y. Furthermore, z + u = 180, so if we can determine u we can determine z. Therefore we can rephrase the question as "What is the degree measure of angle u?".

The question is how do we know that z+u = 180? Thanks for your detail explanation in advance!!

[Guest]

Triangle BCD is isoceles triangle. (BD=CD). The angles opposite to these side will be equal. Thus u = v

We know that : z+v = 180
v=u
So, z+u = 180

[shaji]

z+v=180; v=u,z+u=180

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

(1) v = 74 degrees

(2) w = 32 degrees




The answer is "EACH statement ALONE is sufficient.". The explanation given is pasted below

The question asks us to find the number of degrees in x + y. Since the sum of the angles in any triangle is 180 degrees, we know that x + y + z = 180, so if we can find z we can find x + y. Furthermore, z + u = 180, so if we can determine u we can determine z. Therefore we can rephrase the question as "What is the degree measure of angle u?".

The question is how do we know that z+u = 180? Thanks for your detail explanation in advance!!

[pinal2]

Thanks, that helps.

[StaceyKoprince]

Let us know if you have any more questions!

[mstart7000]

I know the diagram appears to show that AC is a straight line, but how do we know this?

Don't the instructions always state that pictures are not to scale?

If we don't know that AC is a straight line then we don't know that z + v = 180.

Am I missing something simple?

Thanks,
Mike

[tim]

I know the diagram appears to show that AC is a straight line, but how do we know this?

Don't the instructions always state that pictures are not to scale?

If we don't know that AC is a straight line then we don't know that z + v = 180.

Am I missing something simple?

Thanks,
Mike

First, no the instructions do not always indicate that the diagrams are not to scale. Second, you can assume that when something looks like a straight line it is. The rule of thumb is you can assume qualitative information (eg. if AB looks like a straight line it is), but not quantitative information (eg. if A looks like 90 degrees, how do you know it's not 89 or 91?). I know this is not super precise and that there are times when the line between qualitative and quantitative information is blurred, but this is a good rule to follow in general..

[benkriger]

I got this question wrong for the same reason. Its clear both statements are sufficient if in fact ADC is a triangle. But its too much to assume it is. This question should be mended to say: If ABC is a triangle. Specially for a level 500...

[RonPurewal]

I got this question wrong for the same reason. Its clear both statements are sufficient if in fact ADC is a triangle. But its too much to assume it is. This question should be mended to say: If ABC is a triangle. Specially for a level 500...

au contraire, you can always assume that things that look like straight lines are, in fact, straight lines.

[Ineedhelp]

I'm having problem understanding the concept. I want to know if I have this correct.

I'll try to work out the problem from what I've learned, and please jump in and let me know if I'm doing something incorrectly. I want to know if this is correct.

The stem states <BD=<CD, so off hand, I must recognize that this is an Isosceles triangle. Two opposite sides with be equal. So if I don't know this, I'm screwed already.

1) V=74. If I know this is an isosceles triangle: and V=74, therefore U will also equal 74.

U+V=148
Next, Solve for W

W=180-148=32
W=32
180-V=106

From what I know of triangles, they equal 180 degrees.

180-V=Z
Z=106

X+Y+Z=180
X+Y+106=180 (Plug in for Z below)
-106 -106 Subtract Z from both sides.
X+Y =74

This is sufficient to solve the problem.
Why, because Z is known. Therefore X+Y = is determined. We don't care for the value of X or Y.

For Statement 2) W=32, so 180-32=148, 148/2=74,
continue to X+Y+Z=180

Known's
V=74

Solve for Z. 180-V=106
Z=106

X+Y+Z=180
-106 =-106 substitute/subtract for Z
X+Y = 74


Can the MGMAT instructors please specify if I did this correctly.

Thanks.

[RonPurewal]

The stem states <BD=<CD,

Those aren't angles; those are side lengths. Not sure why you're using an angle symbol.

so off hand, I must recognize that this is an Isosceles triangle. Two opposite sides with be equal. So if I don't know this, I'm screwed already.

Not necessarily. I, for one, don't have this fact memorized -- I just think about symmetry.
E.g., once I realize that two sides (or two angles) are the same, I just think about drawing an imaginary line of symmetry down the middle of the triangle. If I do that, I don't have to memorize anything.

[RonPurewal]

1) V=74. If I know this is an isosceles triangle: and V=74, therefore U will also equal 74.

U+V=148
Next, Solve for W

W=180-148=32
W=32
180-V=106

From what I know of triangles, they equal 180 degrees.

180-V=Z
Z=106

X+Y+Z=180
X+Y+106=180 (Plug in for Z below)
-106 -106 Subtract Z from both sides.
X+Y =74

This is sufficient to solve the problem.

Everything in green is irrelevant. Waste of time.

If you have v, you can just find z, from which you can find x + y as described. Why bother with the right-hand triangle?

Remember, FOCUS on a GOAL is the primary thing tested on data sufficiency problems. You don't want to wander all around the diagram finding irrelevant information. You want to identify what you actually NEED to find, and then find things with that specific goal in mind.

In other words, I have a feeling you'd have gotten this part wrong if they hadn't told you that the right-hand triangle is isosceles. Even if there's no information about the right-hand triangle at all, this statement is still sufficient.

For Statement 2) W=32, so 180-32=148, 148/2=74,
continue to X+Y+Z=180

Known's
V=74

Solve for Z. 180-V=106
Z=106

X+Y+Z=180
-106 =-106 substitute/subtract for Z
X+Y = 74

Works.