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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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New post 15 Mar 2018, 23:19
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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
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

Attachment:
2018-03-16_1010.png


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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 1021 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

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

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New post 20 Oct 2019, 10:06
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

Attachment:
2018-03-16_1010.png


Draw a line through the vertex of angle x that is parallel to both l1 and l2. We will see that angle x is the sum of the two given angles of 40 degrees and 30 degrees. Thus angle x = 70 degrees.

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 20 Oct 2019, 10:11
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

Attachment:
2018-03-16_1010.png


x = 180 - (180 - 40 - 30) = 70

IMO A
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Re: In the figure above if l1||l2, what is the value of x?   [#permalink] 20 Oct 2019, 10:11
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