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In the figure above if l1||l2, what is the value of x?

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In the figure above if l1||l2, what is the value of x? [#permalink]

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In the figure above if \(l_1||l_2\), what is the value of x?

A. 70
B. 100
C. 110
D. 150
E. 170

[Reveal] Spoiler:
Attachment:
2018-03-16_1010.png
2018-03-16_1010.png [ 6.61 KiB | Viewed 393 times ]
[Reveal] Spoiler: OA

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In the figure above if l1||l2, what is the value of x? [#permalink]

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New post 15 Mar 2018, 23:19
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Bunuel wrote:
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In the figure above if \(l_1||l_2\), what is the value of x?

A. 70
B. 100
C. 110
D. 150
E. 170

[Reveal] Spoiler:
Attachment:
2018-03-16_1010.png


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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the figure above if l1||l2, what is the value of x? [#permalink]

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New post 15 Mar 2018, 23:53
I got A - 70°, you can complete the top triangle as 30°, 40° and 110° because l1 and l2 are parallel, x = 180° - 110° which is 70°
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Re: In the figure above if l1||l2, what is the value of x? [#permalink]

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New post 16 Mar 2018, 08:35
Bunuel wrote:
In the figure above if \(l_1||l_2\), what is the value of x?

A. 70
B. 100
C. 110
D. 150
E. 170

Attachment:
2018-03-16_1010ed.png
2018-03-16_1010ed.png [ 10.8 KiB | Viewed 223 times ]

A couple of other ways to approach . . .

\(l_1\) and \(l_2\) are cut by a transversal

Alternate interior angles are congruent.
Lower right angle = \(40°\)
Other angle of lower triangle, given = \(30°\)

1) \(x\) = exterior angle
Exterior angle \(x\) = sum of opposite interior angles of lower triangle
Exterior angle \(x\) \(= (30° + 40°) =\) \(70°\)

OR

2) Straight line: Third angle of lower ∆ + \(x = 180°\)
Interior angles of a triangle sum to 180°
Lower ∆'s third angle = \(110°\)
(\((180° - 30° - 40°) = 110°\) = third angle))

Third angle lies on a straight line with \(x\)
\(110° + x° = 180°\)
\(x = 70°\)


Answer A
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Re: In the figure above if l1||l2, what is the value of x? [#permalink]

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New post 18 Mar 2018, 10:40
Bunuel wrote:
Image
In the figure above if \(l_1||l_2\), what is the value of x?

A. 70
B. 100
C. 110
D. 150
E. 170

[Reveal] Spoiler:
Attachment:
The attachment 2018-03-16_1010.png is no longer available


Drawing a additional parallel line l1 and l2 and using property of equal alternate angle between 2 parallel line

we get x= 30 +40
x=70
Answer : A
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Capture.PNG [ 6.93 KiB | Viewed 129 times ]


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Re: In the figure above if l1||l2, what is the value of x?   [#permalink] 18 Mar 2018, 10:40
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