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# Four lines intersect as shown in the figure above. If p = 50, what is

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Math Expert
Joined: 02 Sep 2009
Posts: 54370
Four lines intersect as shown in the figure above. If p = 50, what is  [#permalink]

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01 Aug 2017, 05:03
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Four lines intersect as shown in the figure above. If p = 50, what is the value of x + y?

(A) 230
(B) 240
(C) 260
(D) 270
(E) 300

Attachment:

2017-08-01_1350_002.png [ 12.13 KiB | Viewed 1278 times ]

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Re: Four lines intersect as shown in the figure above. If p = 50, what is  [#permalink]

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01 Aug 2017, 07:23
Quote:

Since p=50, and the sum of angles in a straight line is 180,
the unknown angle(lets call it B) is 40 degree.
The angle within the triangle (which is also a corresponding angle of B) is equal to 40 degree.

Since the triangle is right angled, the third angle adjacent to x and y is 50 degree
We know that the sum of angles in a straight line is 180 degree.
Therefore, x=y= 130 degree, and its sum(x+y) = 260(Option C)
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Four lines intersect as shown in the figure above. If p = 50, what is  [#permalink]

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01 Aug 2017, 18:26
Bunuel wrote:

Four lines intersect as shown in the figure above. If p = 50, what is the value of x + y?

(A) 230
(B) 240
(C) 260
(D) 270
(E) 300

Attachment:
The attachment 2017-08-01_1350_002.png is no longer available

Attachment:

pxy parallel lines.png [ 23.21 KiB | Viewed 962 times ]

The right angles indicate that the two horizontal lines are parallel.

Angle p and the yellow-shaded angle are vertical angles, hence equal.
p = 50
yellow = 50

The yellow angle and the green angle are alternate interior angles of parallel lines cut by a transversal.
yellow = 50
green = 50

Finally, the green and blue angles are vertical angles and hence equal.
green = 50
blue = 50

Angles x, y, green, and blue surround a single point with 360 degrees.

green + blue = 100

x + y + green + blue = 360

x + y + 100 = 360

x + y = 360 - 100

x + y = 260

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Re: Four lines intersect as shown in the figure above. If p = 50, what is  [#permalink]

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02 Aug 2017, 13:32
Bunuel wrote:

Four lines intersect as shown in the figure above. If p = 50, what is the value of x + y?

(A) 230
(B) 240
(C) 260
(D) 270
(E) 300

Attachment:
2017-08-01_1350_002.png

First of all, we note that the two lines that look like horizontal lines are parallel, since they each intersect the line that looks like a vertical line at a right angle.

Since angle p is corresponding to the angle of the triangle (let’s call it angle z) that is adjacent to both angles x and y, we have p = z. Since p = 50, z = 50. Let w denote the angle that is vertical to z. Now x, y, z, and w form a whole rotation, that is x + y + z + w = 360. Since z = w = 50, x + y + 100 = 360, and thus, x + y = 260.

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Re: Four lines intersect as shown in the figure above. If p = 50, what is   [#permalink] 02 Aug 2017, 13:32
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