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In the figure above, if lines m, n, p are parallel, what is the sum of

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In the figure above, if lines m, n, p are parallel, what is the sum of [#permalink]

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New post 01 Aug 2017, 04:07
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In the figure above, if lines m, n, p are parallel, what is the sum of x + y?

(A) 40
(B) 60
(C) 80
(D) 90
(E) 100

[Reveal] Spoiler:
Attachment:
2017-08-01_1351_001.png
2017-08-01_1351_001.png [ 6.06 KiB | Viewed 625 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, if lines m, n, p are parallel, what is the sum of [#permalink]

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New post 01 Aug 2017, 06:10
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Extend the line from m to n, a triangle is formed.
The line which is formed at the intersection of the line n and the extended line is 180-x
Therefore, the angle inside the triangle is x.

In the triangle formed, the angle on the line is 180-(40+60) = 80 degree.
Since the sum of angles in a triangle is 180 degree,
x+y+80 = 180
x+y = 100 degree(Option E)
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Re: In the figure above, if lines m, n, p are parallel, what is the sum of [#permalink]

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New post 01 Aug 2017, 06:17
Bunuel wrote:
Image
In the figure above, if lines m, n, p are parallel, what is the sum of x + y?

(A) 40
(B) 60
(C) 80
(D) 90
(E) 100

[Reveal] Spoiler:
Attachment:
2017-08-01_1351_001.png


Let us name straight line between m and n as R
P makes same angle on m as on n . that means P makes 40 degree angle at m
hence X=4o
Let us name straight line between n and p as T
p makes same angle on n as on p . that means T makes 60 degree angle at p
hence Y=60
x+y=40+60=100
hence option (E)
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In the figure above, if lines m, n, p are parallel, what is the sum of [#permalink]

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New post 01 Aug 2017, 17:01
Bunuel wrote:
Image
In the figure above, if lines m, n, p are parallel, what is the sum of x + y?

(A) 40
(B) 60
(C) 80
(D) 90
(E) 100

[Reveal] Spoiler:
Attachment:
2017-08-01_1351_001.png

Lines m, n, and p are parallel lines that are cut by two transversals. (Extend both slanted lines to visualize.)

Alternate interior angles of parallel lines cut by a transversal are equal.

x and 40° are alternate interior angles. x = 40

y and 60° are alternate interior angles. y = 60

x + y = 100

Answer E
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Re: In the figure above, if lines m, n, p are parallel, what is the sum of [#permalink]

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New post 02 Aug 2017, 12:31
Bunuel wrote:
Image
In the figure above, if lines m, n, p are parallel, what is the sum of x + y?

(A) 40
(B) 60
(C) 80
(D) 90
(E) 100

[Reveal] Spoiler:
Attachment:
2017-08-01_1351_001.png


Since lines m, n, and p are parallel, we see that x = 40 and y = 60; thus, x + y = 100.

Answer: E
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Re: In the figure above, if lines m, n, p are parallel, what is the sum of   [#permalink] 02 Aug 2017, 12:31
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