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Parallel lines p and q are intersected by lines m and n as shown. What

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Parallel lines p and q are intersected by lines m and n as shown. What  [#permalink]

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08 Aug 2017, 01:45
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Parallel lines p and q are intersected by lines m and n as shown. What is the value of x + y?

(A) 140
(B) 150
(C) 160
(D) 170
(E) 180

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2017-08-08_1254.png [ 9.48 KiB | Viewed 3638 times ]

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Re: Parallel lines p and q are intersected by lines m and n as shown. What  [#permalink]

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08 Aug 2017, 01:52
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Bunuel wrote:
Parallel lines p and q are intersected by lines m and n as shown. What is the value of x + y?

(A) 140
(B) 150
(C) 160
(D) 170
(E) 180

Bunuel Diagram missing
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Luckisnoexcuse
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Re: Parallel lines p and q are intersected by lines m and n as shown. What  [#permalink]

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08 Aug 2017, 01:55
Luckisnoexcuse wrote:
Bunuel wrote:
Parallel lines p and q are intersected by lines m and n as shown. What is the value of x + y?

(A) 140
(B) 150
(C) 160
(D) 170
(E) 180

Bunuel Diagram missing

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Edited. Thank you.
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Parallel lines p and q are intersected by lines m and n as shown. What  [#permalink]

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08 Aug 2017, 02:39

Since parallel lines p and q are intersected by lines m and n,
angle formed by line m on line p is 60(lets call this a)
and angle formed by line n on line p is 130(lets call this b)
These are corresponding angles for the parallel lines m and n.

Now, we know that the sum of angles in a straight line is 180 degree.
There a + x = b + y = 180
Substituting these values of a and b, we get x = 120 and y = 50
Therefore, x+y = 170(Option D)
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Parallel lines p and q are intersected by lines m and n as shown. What  [#permalink]

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08 Aug 2017, 14:48
Bunuel wrote:

Parallel lines p and q are intersected by lines m and n as shown. What is the value of x + y?

(A) 140
(B) 150
(C) 160
(D) 170
(E) 180

Attachment:
2017-08-08_1254.png

y + 130 = 180 because they are same-side interior angles of parallel lines cut by a transversal, which are always supplementary.

y = 50

x + 60 = 180 because x's congruent vertical angle and 60 are also same-side interior angles.

x = 120

120 + 50 = 170

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Re: Parallel lines p and q are intersected by lines m and n as shown. What  [#permalink]

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10 Aug 2017, 10:53
Bunuel wrote:

Parallel lines p and q are intersected by lines m and n as shown. What is the value of x + y?

(A) 140
(B) 150
(C) 160
(D) 170
(E) 180

Attachment:
2017-08-08_1254.png

Since the angle next to angle x is a corresponding angle to the angle measuring 60 degrees, it also measures 60 degrees. Since it and angle x are supplementary, angle x = 180 - 60 = 120 degrees.

Since angle y and the angle measuring 130 degrees are on the same side of a transversal of two parallel lines, they are supplementary, and thus angle y = 180 - 130 = 50 degrees.

Thus, x + y = 120 + 50 = 170.

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Re: Parallel lines p and q are intersected by lines m and n as shown. What   [#permalink] 10 Aug 2017, 10:53
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