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In the figure above, if lines m and n are parallel, then x =

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In the figure above, if lines m and n are parallel, then x =  [#permalink]

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New post 01 Aug 2017, 04:53
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A
B
C
D
E

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  25% (medium)

Question Stats:

79% (00:42) correct 21% (00:22) wrong based on 36 sessions

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In the figure above, if lines m and n are parallel, then x =

(A) 20
(B) 50
(C) 150
(D) 140
(E) 160

Attachment:
2017-08-01_1349_001.png
2017-08-01_1349_001.png [ 6.58 KiB | Viewed 631 times ]

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Re: In the figure above, if lines m and n are parallel, then x =  [#permalink]

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New post 01 Aug 2017, 05:35
Bunuel wrote:
Image


Since line m and n are parallel to each other, one of the angles in the right angled triangle
which has two of its vertices on line n is 70 degree.

Hence, the third angle of the triangle is 180 - 90 - 70 = 20 degree.

The angle x is supplementary to the third angle of this triangle
Therefore, x = 180 - 20 = 160(Option E)
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In the figure above, if lines m and n are parallel, then x =  [#permalink]

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New post 01 Aug 2017, 07:12
Say the 3rd line name is P.
Angle opposite to 90 degree ( on the line P ) is 90 degree

Since line m and n are parallel to each other, angle made my line P on line n is also 70 degree.
Now in this triangle we know 2 angles 90 degree and 70 degree
sum of the angles in a triangle is 180
hence third angle =180-90-70=20
The angle x is supplementary to the third angle of this triangle
Therefore, x = 180 - 20=160

hence (E)
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Re: In the figure above, if lines m and n are parallel, then x =  [#permalink]

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New post 02 Aug 2017, 13:29
Bunuel wrote:
Image
In the figure above, if lines m and n are parallel, then x =

(A) 20
(B) 50
(C) 150
(D) 140
(E) 160

Attachment:
2017-08-01_1349_001.png


We see that we have two parallel lines, lines m and n, cut by a transversal, which we will denote as line t. We also see that we have a triangle formed by lines n and t and another line. Finally, we see that x is an exterior angle of this triangle, and the measure of angle x is the sum of the two remote interior angles of the triangle. One of these two angles is 90 degrees, since it’s supplemental to a right angle. The other remote interior angle is 70 degrees, since it’s the corresponding angle to the 70-degree angle shown. Thus, x = 90 + 70 = 160 degrees.

Answer: E
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Re: In the figure above, if lines m and n are parallel, then x = &nbs [#permalink] 02 Aug 2017, 13:29
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