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01 Aug 2017, 05:03
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C
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Difficulty:
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94% (01:06) correct
6%
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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 3812 times ]
01 Aug 2017, 07:23
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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)
01 Aug 2017, 18:26
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Bunuel
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 3236 times ]
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
Answer C
