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The lines m, l, and n intersect at point Q. What are the mea

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

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New post Updated on: 15 Jun 2013, 05:44
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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

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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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New post 15 Jun 2013, 06:06
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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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New post 15 Jun 2013, 06:14
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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Re: The lines m, l, and n intersect at point Q. What are the mea  [#permalink]

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New post 15 Jun 2013, 06:20
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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
Lines.png [ 54.08 KiB | Viewed 1794 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.

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

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New post 10 Dec 2013, 15:02
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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New post 24 Jan 2014, 00:47
(1) z = 1/2x². No more info about x or z, IS.
(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]

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