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655-705 (Hard)|   Geometry|      
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In the figure above, lines a and b are parallel. What is x? 20 Jun 2018, 06:41
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

60% (02:34) correct 40% (02:53) wrong based on 93 sessions

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In the figure above, lines a and b are parallel. What is x?

A) 9
B) 18
C) 36
D) 45
E) 54


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E
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In the figure above, lines a and b are parallel. What is x? 20 Jun 2018, 07:59
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In the figure above, lines a and b are parallel. What is x?

A) 9
B) 18
C) 36
D) 45
E) 54


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gmatbusters.jpg
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Hi All,

Hope everyone is doing great! Posting after a long time off study. :)

IMO Option (E).

Solution:

1. The internal angles of the traingle come out to be (180 - x - 2y) & (180 - 3x) & 6y. Sum of internal angles of a traingle equals 180 deg gives us -

(180 - 3x) + 6y + (180 - x - 2y) = 180
x = y + 45 (1)

2. The angles 3x and 2y are supplementary. Hence

3x + 2y = 180
y = 90 - 3x/2 (2)

Substitute in equation (1) to get -

x = 90 - 3x/2 + 45
5x/2 = 135
x = 270/5 or 540 /10
x = 54 deg

Hence Option (E).

Best,
Gladi
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In the figure above, lines a and b are parallel. What is x? 20 Jun 2018, 11:22
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In the figure above, lines a and b are parallel. What is x?

A) 9
B) 18
C) 36
D) 45
E) 54


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gmatbusters.jpg
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From the figure we have 3x + 2y = 180 & 3x = 2x +6y ( external angle)

We get x = 6y, substituting in 3x + 2y = 180 , we get y = 9

Hence x = 54

Answer E.

Thanks,
GyM
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In the figure above, lines a and b are parallel. What is x? 20 Jun 2018, 22:44
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In the figure above, lines a and b are parallel. What is x?

A) 9
B) 18
C) 36
D) 45
E) 54
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gmatbusters2.jpg [ 16.3 KiB | Viewed 2954 times ]
• \(x = 6y\)
At vertex C, \(x\) is a corresponding angle of parallel lines cut by a transversal.
And at C, \(x\) and \(6y\) are equal vertical angles.
\(x=6y\)
\(y=\frac{x}{6}\)


• \(3x + 2y = 180\)
Alternate interior angle with measure \(2y\)
is at vertex A, adjacent to \(3x\)

\(3x\) and \(2y\) lie on a straight line.
Solve for \(x\)

Straight line: \(3x + 2y = 180\)
Substitute: \(y=\frac{x}{6}\)
\(3x +2(\frac{x}{6})=180\)
\(18x + 2x = 1,080\)
\(20x = 1,080\)
\(x=54\)

Answer E
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In the figure above, lines a and b are parallel. What is x? 20 Jun 2018, 23:10
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Solution



To find:
    • We need to find the value of x.

Approach and Working:



    • \(x^0= 6y^0\) as both are vertically opposite angles.
      o Thus, \(2y^0 = \frac{x}{3}^0\)

    • Hence, \(3x^0+\frac{x}{3}^0= 180^0\)
      o \(\frac{10x}{3}^0=180^0\)
      o \(x= 54^0\)

Hence, the correct answer is option E.

Answer: E
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In the figure above, lines a and b are parallel. What is x? 29 Dec 2020, 05:24
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