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

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Math Expert
Joined: 02 Sep 2009
Posts: 58988
In the figure above if l1||l2, what is the value of x?  [#permalink]

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15 Mar 2018, 23:19
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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 [ 6.61 KiB | Viewed 1271 times ]

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Math Expert
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Posts: 58988
In the figure above if l1||l2, what is the value of x?  [#permalink]

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15 Mar 2018, 23:19
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_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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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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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 [ 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 $$x$$
$$110° + x° = 180°$$
$$x = 70°$$

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

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18 Mar 2018, 10:40
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:
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
Attachments

Capture.PNG [ 6.93 KiB | Viewed 926 times ]

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

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20 Oct 2019, 10:06
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_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.

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

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20 Oct 2019, 10:11
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_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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