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In the figure above, if z = 50, then x + y =

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In the figure above, if z = 50, then x + y = [#permalink] New post 27 Dec 2012, 06:09
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B
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In the figure above, if z = 50, then x + y =

(A) 230
(B) 250
(C) 260
(D) 270
(E) 290
[Reveal] Spoiler: OA
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Re: In the figure above, if z = 50, then x + y = [#permalink] New post 27 Dec 2012, 16:36
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Adding on to what Bunuel has explained,

Alternate angles between two parallel lines are equal, so angle Z is equal to Red angle = 50

Sum of all angles in a Triangle = 180 so , 90+50 (Red)+Blue = 180
Blue Angle = 40, hence X = 180-40 = 140 --> A

Sum of all interior angles in a Quadrilateral is 360,

So z+y+2 Right angles = 360
50+Y+90+90 = 360
Y = 360-230 = 130 --> B

From Statement A and Statement B we get x+y = 140+130 = 270

Ans D
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Re: In the figure above, if z = 50, then x + y = [#permalink] New post 18 Jun 2013, 22:50
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My 30 second solution:

sum of angles in triangle = 180

Sum of angles in small triangle:
(180-y) + (180-x) + 90 = 180
--> x+y = 270

IMO the information z = 50 is not needed to calculate x+y if we know that the two vertical lines are parallel and hence we have a right angle in the smaller triangle.
Let me know if my reasoning is wrong.

Cheers
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Re: In the figure above, if z = 50, then x + y = [#permalink] New post 19 Jun 2013, 01:18
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kingflo wrote:
My 30 second solution:

sum of angles in triangle = 180

Sum of angles in small triangle:
(180-y) + (180-x) + 90 = 180
--> x+y = 270

IMO the information z = 50 is not needed to calculate x+y if we know that the two vertical lines are parallel and hence we have a right angle in the smaller triangle.
Let me know if my reasoning is wrong.

Cheers


An exterior angle of a triangle ( In this case y) is always equal to the sum of the opposite interior angles [ In this case 90 degrees and (180-x)]

Thus, y = 90 + 180-x --> x+y = 270

So, yes you are correct.
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Re: In the figure above, if z = 50, then x + y = [#permalink] New post 29 Nov 2013, 12:17
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Yes, the setup of y = 90 + (180 - x)

is a great way to solve this question without knowing x or y.

If you are not familiar with spotting exterior angles and prefer to do things the old school way - well, there's plenty of information in the diagram from which you can gather together to find the actual value of y. And then from there you can solve for x and then add up x and y.

Either method works fine.

Below is a video demonstration of the adding up x and y approach:

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In the figure above, if z = 50, then x + y = [#permalink] New post 27 Dec 2012, 06:19
Expert's post
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In the figure above, if z = 50, then x + y =

(A) 230
(B) 250
(C) 260
(D) 270
(E) 290

Look at the diagram below:
Attachment:
Angles2.png
Angles2.png [ 10.57 KiB | Viewed 2760 times ]
Notice that red angles are equal, thus red angle in smaller triangle is 50 degrees as well: (red angle) = 50.

Now, smaller triangle is right angled, thus (red angle) + (blue angle) = 90 --> 50 + (blue angle) = 90 --> (blue angle) = 40.

Next, since x + (blue angle) = 180, then x = 140. Also, since (red angle) = 180 - y, then, y = 130.

x + y = 140 + 130 = 270.

Answer: D.
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Re: In the figure above, if z = 50, then x + y = [#permalink] New post 24 Jul 2014, 23:06
I think I don't understand an important part in this question here.. What is meant by x + y ? I thought it is the value of the angles? (blue + red one)

So i would have calculated 40 + 130. Can anyone help me ?
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Re: In the figure above, if z = 50, then x + y = [#permalink] New post 25 Jul 2014, 02:09
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lou34 wrote:
I think I don't understand an important part in this question here.. What is meant by x + y ? I thought it is the value of the angles? (blue + red one)

So i would have calculated 40 + 130. Can anyone help me ?


Yes, the question asks about the sum of the measures of angles x and y. x = 140° and y = 130°, so the sum is 270°.

Complete solution is here: in-the-figure-above-if-z-50-then-x-y-144792.html#p1161593

Hope it helps.
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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 figure above, if z = 50, then x + y =   [#permalink] 25 Jul 2014, 02:09
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