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

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In the diagram above, line m and line n are parallel. Given that angl  [#permalink]

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New post 05 Mar 2015, 08:57
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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


Kudos for a correct solution.

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In the diagram above, line m and line n are parallel. Given that angl  [#permalink]

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New post 05 Mar 2015, 21:15
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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]

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New post 06 Mar 2015, 04:32
3
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
lines.png [ 3.21 KiB | Viewed 1769 times ]

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Re: In the diagram above, line m and line n are parallel. Given that angl  [#permalink]

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New post 08 Mar 2015, 13:48
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 1762 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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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the diagram above, line m and line n are parallel. Given that angl  [#permalink]

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Re: In the diagram above, line m and line n are parallel. Given that angl   [#permalink] 09 Oct 2018, 06:00
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