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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The lines m, l, and n intersect at point Q. What are the mea

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Director  Joined: 29 Nov 2012
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The lines m, l, and n intersect at point Q. What are the mea  [#permalink]

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4 00:00

Difficulty:   35% (medium)

Question Stats: 76% (02:06) correct 24% (01:39) wrong based on 155 sessions

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The lines m, l, and n intersect at point Q. What are the measures of the six angles formed by these lines?

(1) The measure of z is one half the square of the measure of x.

(2) v + w = 130

Originally posted by fozzzy on 15 Jun 2013, 05:43.
Last edited by Bunuel on 15 Jun 2013, 05:44, edited 1 time in total.
Edited the question.
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Re: The lines m, l, and n intersect at point Q. What are the mea  [#permalink]

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The lines m, l, and n intersect at point Q. What are the measures of the six angles formed by these lines?

From the image we can determine that: Y=V, X=W and T=Z and that their sum is 360.
2V+2X+2Z=360 or V+X+Z=180

(1) The measure of z is one half the square of the measure of x.
Given that $$V+X+Z=180$$
$$Z=\frac{1}{2}*X^2$$
$$V+\frac{1}{2}*X^2+X=180$$
Not sufficient

(2) v + w = 130
Clearly not sufficient

1+2)Since w=x we can rewrite 2 as v+x=130. From 1 we know that $$V+\frac{1}{2}*X^2+X=180$$ and combining the equations we get $$X^2=100$$ $$X=10$$. So $$V=120$$ and $$Z=180-120-10=50$$.
Sufficient
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Re: The lines m, l, and n intersect at point Q. What are the mea  [#permalink]

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fozzzy wrote:
Attachment:
421.jpg
The lines m, l, and n intersect at point Q. What are the measures of the six angles formed by these lines?

(1) The measure of z is one half the square of the measure of x.

(2) v + w = 130

F.S 1 clearly Insufficient. We just know that $$z = 0.5*x^2$$

F.S 2 tells us that z = t= 50. Insufficiet.

On combining both the statements, we know that z = 50 degrees and $$x^2$$ = 2*50 = 100. Thus, x = w =10 degrees, v = 120 degrees and z = 50 degrees. Sufficient.
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The lines m, l, and n intersect at point Q. What are the measures of the six angles formed by these lines?
Attachment: Lines.png [ 54.08 KiB | Viewed 1951 times ]

All the same color angles are equal. Thus we need to find the measures of say z, w, and v, while knowing that $$z+w+v=180$$.

(1) The measure of z is one half the square of the measure of x --> $$z=\frac{x^2}{2}$$ --> $$z=\frac{w^2}{2}$$. Not sufficient.

(2) v + w = 130 --> $$z=50$$ (from $$z+w+v=180$$). Not sufficient.

(1)+(2) $$z=50$$ --> $$w=10$$ (from $$z=\frac{w^2}{2}$$) and $$v=120$$. Sufficient.

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Re: The lines m, l, and n intersect at point Q. What are the mea  [#permalink]

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The lines m, l, and n intersect at point Q. What are the measures of the six angles formed by these lines?

(1) The measure of z is one half the square of the measure of x.

Keep in mind that we have lots of vertical angles here...

z = 1/2 x^2 which doesn't tell us a whole lot because we don't know what z or x are. Insufficient.

(2) v + w = 130
if v + w = 130 then x + y = 130 as well because they are opposite angles. z + t are vertical angles and they equal the remainder of angles. z + t = 360 - (x + y) - (v + w) --> z + t = 360 - 130 - 130. z + t = 100 z = t because they are vertical angles. so z, t = 50 But we don't know the rest of the measures. Insufficient.

1 +2) If z = 1/2 x^2 then 50 = 1/2 x^2 --> 100 = x^2 --> x = 10. The opposite angle to x, w = 10 as well.

x + y = 130 --> 10 + y = 130 y = 120. y and it's opposite angle v = 120. Sufficient.

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Re: The lines m, l, and n intersect at point Q. What are the mea  [#permalink]

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(2) v+w= 130, hence t=180-130 = 50. But v could be 30 and w 100 or 90 and 40. IS.

Together: z = t = 50 = 1/2x² => x = w = 10 ==> y = v = 180 - 50 - 10 = 120. SUFF.

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_________________ Re: The lines m, l, and n intersect at point Q. What are the mea   [#permalink] 01 Sep 2018, 04:05
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