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If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°

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If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 04 Sep 2016, 05:35
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If in the figure above, l1 and l2 are parallel, what is x?

A. 30°
B. 40°
C. 50°
D. 55°
E. 70°

Attachment:
T10407.png
T10407.png [ 4.24 KiB | Viewed 3050 times ]

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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 04 Sep 2016, 06:46
IMO B.

When we combine the two lines l1 and l2 with a straight line that forms a quadrilateral with a right angle at l2 and straight line drawn.

360 - (110+110+90 ) = 50.

x = 90-50 = 40.
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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 04 Sep 2016, 07:26
If you extrapolate the line that starts from l1, to meet l2. It forms a triangle with 70, 70 and x

70+70+x=180

x=40

Ans B
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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 04 Sep 2016, 10:44
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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 04 Sep 2016, 13:32
1
Bunuel wrote:
Image
If in the figure above, l1 and l2 are parallel, what is x?

A. 30°
B. 40°
C. 50°
D. 55°
E. 70°

Attachment:
The attachment T10407.png is no longer available


Answer will be (B) 40°

Attachment:
T10407.png
T10407.png [ 8.79 KiB | Viewed 2522 times ]

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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 06 Sep 2016, 12:40
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Top Contributor
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Bunuel wrote:
Image
If in the figure above, l1 and l2 are parallel, what is x?

A. 30°
B. 40°
C. 50°
D. 55°
E. 70°

Attachment:
T10407.png


Another approach is to add a third parallel line.

Given:
Image

So, let's draw a third parallel line (in green)....
Image

Since that angle at that point is given as 110 degrees, we know that a + b = 110

At this point, we should recognize that the two highlighted angles (below) are on the same side of the transversal, which means they must ADD to 180.
Image

So, angle b must equal 70 degrees.....
Image

Since we already know that a + b = 110, we can conclude that angle a must equal 40 degrees...
Image

Finally, since the two highlighted angles (below) are on the opposite sides of the transversal, they must be EQUAL.
Image

So, angle x = 40 degrees.

Answer:

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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50°  [#permalink]

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New post 24 Nov 2017, 10:32
Top Contributor
Bunuel wrote:
Image
If in the figure above, l1 and l2 are parallel, what is x?

A. 30°
B. 40°
C. 50°
D. 55°
E. 70°

Attachment:
T10407.png


IMPORTANT: the diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.
So, if we're not sure how to solve the question, we can use the above fact to ESTIMATE the value of x (or at least eliminate some of the answer choices to help improve our chances of a correct guess).

Cheers,
Brent
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Re: If in the figure above, l1 and l2 are parallel, what is x? 30° 40° 50° &nbs [#permalink] 24 Nov 2017, 10:32
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