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In the diagram above, line m and line n are parallel. Given that angl

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Bunuel
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In the diagram above, line m and line n are parallel. Given that angl [#permalink] New post   05 Mar 2015, 09:57
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In the diagram above, line m and line n are parallel. Given that angle a = 40° and angle c = 55°, what is the measure of angle b?

A. 85°
B. 90°
C. 95°
D. 100°
E. angle b cannot be determined from the information given


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C
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chetan2u
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In the diagram above, line m and line n are parallel. Given that angl [#permalink] New post   05 Mar 2015, 22:15
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Attachment:
New Microsoft Office Word Document 12.docx [20.51 KiB]
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Bunuel wrote:
Attachment:
The attachment anplotg_img2.png is no longer available
In the diagram above, line m and line n are parallel. Given that angle a = 40° and angle c = 55°, what is the measure of angle b?

A. 85°
B. 90°
C. 95°
D. 100°
E. angle b cannot be determined from the information given


Kudos for a correct solution.


hi,
ans C.. 95
at any point between the two parallel lines, the angle formed by the two points at the center will be equal to the sum of angle made by these lines with parallel lines(a,c in this case).. a+c=40+55=95..
for explanation of above point ,refer to the solution below
refer the attached drawing when the two points on the parallel lines are joined..
in the drawing a+x+c+y= 180(consecutive interior angles are 180 between two parallel lines)..
or 40+x+55+y=180.. x+y=85...
in the triangle formed by angles x,y and b, x+y+b=180..
or 85+b=180....
so b=95
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Re: In the diagram above, line m and line n are parallel. Given that angl [#permalink] New post   06 Mar 2015, 05:32
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I also go with C.

Since the lines are parallel we get the following shape (i am sorry that it looks so ugly...).
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lines.png [ 3.21 KiB | Viewed 5580 times ]

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Re: In the diagram above, line m and line n are parallel. Given that angl [#permalink] New post   08 Mar 2015, 14:48
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Bunuel wrote:
Attachment:
The attachment anplotg_img2.png is no longer available
In the diagram above, line m and line n are parallel. Given that angle a = 40° and angle c = 55°, what is the measure of angle b?

A. 85°
B. 90°
C. 95°
D. 100°
E. angle b cannot be determined from the information given


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Imagine we constructed a new line, parallel to lines m & n, through the vertex of the “crook” between the lines. This splits angle b into two smaller angles, b1 & b2.
Attachment:
anplotg_img5.png
anplotg_img5.png [ 9.62 KiB | Viewed 5521 times ]

Notice, by the parallel lines properties, b1 = a and b2 = c, so b = b1 + b2 = a + c. This means b = 40° + 55° = 95°.

Answer = C
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Re: In the diagram above, line m and line n are parallel. Given that angl [#permalink] New post   12 Jun 2022, 00:03
If we draw a line passing from point b, the line would be parallel to the given lines m and n. Therefore the angle b would be the sum of angle 'a' and angle 'b' which is 40 + 55 = 95 degrees.
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Re: In the diagram above, line m and line n are parallel. Given that angl [#permalink] New post   08 Jul 2023, 15:56
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Re: In the diagram above, line m and line n are parallel. Given that angl [#permalink]
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