Two straight lines intersect to form the angles above. If the measure

Question

Linesproblem.png Two straight lines intersect to form the angles above. If the measure of angle x is three times the measure of angle y, what is the measure of angle z? A. 45 B. 60 C. 120 D. 135 E. 240 Kudos for a correct solution .

Ankur9 · Answer

We have 2 equations from this:
1. z + y = 180
2. x + y = 180
Given: x = 3y
Put the value of x in eq2.
4y = 180---> y = 45
Put the value of y in eq1.
z = 135.

kdatt1991 · Answer

From the question stem we are told that x = 3y. From the diagram we can deduce that x + y = 180 and that y + z = 180. Therefore x + y = y + z....... which means that x = z. So we can say that z = x = 3y. We also know that y + (3y) = 180. After we solve for y, where 4y = 180...... y = 45. Therefore 3y = z = 45*3 = 135. I think the answer should be D! Please consider giving me KUDOS if you felt this post was helpful! Thanks.

EMPOWERgmatRichC · Answer

Hi All,

Most Test Takers would approach this question with a combination of Geometry rules and a bit of Algebra, which is fine. It's a relatively straight-forward prompt, so solving it in that way would be okay. Here's something to consider though: is "your way" to answer this question the fastest way?

The answers to this question are numbers, and since the prompt asks for just one angle (angle Z), one of those numbers MUST be the answer. I'm going to TEST THE ANSWERS.

We'll need to use a few Geometry rules along the way.

1) X+Y = 180 degrees
2) X = Z since opposite angles are equal.

We're told that X is 3 TIMES Y. We're asked for Angle Z (which is the same as asking for the Angle X).

Since X is 3 times Y, X is clearly a LOT bigger than Y (and must be bigger than 90 degrees. Eliminate A and B.
X+Y = 180 degrees, so X cannot = 240. Eliminate E.

Since X + Y = 180
If X = 120, then Y would = 60, but here X is TWICE Y (and it needs to be THREE TIMES Y). Eliminate C.

There's only only answer left.

Final Answer:  D

Many Test Takers focus on the practice questions that they get wrong, without thinking about how they're approaching the questions that they get correct. Getting a question correct is a good thing, but getting it correct in the fastest way possible is the better thing.

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

peachfuzz · Answer

When I first saw the question I noted that angles x and z were equal opposite vertical angles. I then immediately jumped into the algebraic solution with 180/4 and then 180-45. Both would have been relatively fast, but it is interesting to see a more or less conceptual approach vs brute force algebra

DesiGmat · Answer

Here we go:

x is three times the measure of angle y (given)

x = 3y ----(1)

x = z (vertically opposite angles) ---(2)

Now,

x + y = 180 (Linear angle property)

From (1)

3y + y = 180 ---> y = 45 ----> x = 135

From (2)

z = 135

option D is correct

chetan2u · Answer

Hi,
I think in this specific Q, it is much better to go by algebric method for reasons..
1) it will take much lesser time as compared to elimination.
2) the confidence level, during exam, will be way higher if you get the correct ans and find it in choices, rather than elimination, which can always leave a doubt in ur mind..
specially in this Q, when it is straight forward.. and seeing a right ans in choices helps you to approach next Q with way more confidence.

PareshGmat · Answer

Answer = D. 135 Linesproblem.png X = Z = 180 - 45 = 135 X = Z as they are vertically opposite angles

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Since lines x and y will add to a total of 180 degrees, you have two equations to work with:

x + y = 180

x = 3y

This means you can substitute 3y for x in order to solve for y:

3y + y = 180

4y = 180

y = 45

And since z will also sum with y to 180, then z must be 180 - 45 = 135 degrees.

bumpbot · Answer

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Two straight lines intersect to form the angles above. If the measure

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Two straight lines intersect to form the angles above. If the measure

Prep Toolkit

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