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Difficulty:
25%
(medium)
Question Stats:
77% (02:04) correct
23%
(01:39)
wrong
based on 179
sessions
History
Date
Time
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Not Attempted Yet
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(1) The measure of z is one half the square of the measure of x.
(2) v + w = 130
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
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
15 Jun 2013, 06:14
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fozzzy
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.
