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The lines m, l, and n intersect at point Q. What are the mea
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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
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15 Jun 2013, 06:06
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 = 130Clearly 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 \(Z=18012010=50\). Sufficient
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Re: The lines m, l, and n intersect at point Q. What are the mea
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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
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15 Jun 2013, 06:20
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. Answer: C.
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Re: The lines m, l, and n intersect at point Q. What are the mea
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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
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24 Jan 2014, 00:47
(1) z = 1/2x². No more info about x or z, IS. (2) v+w= 130, hence t=180130 = 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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