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

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Manager
Joined: 02 Dec 2012
Posts: 178
In the figure above, if z = 50, then x + y = [#permalink]

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27 Dec 2012, 07:09
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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
Math Expert
Joined: 02 Sep 2009
Posts: 39751
In the figure above, if z = 50, then x + y = [#permalink]

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27 Dec 2012, 07:19
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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 [ 10.57 KiB | Viewed 12875 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.

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Posts: 65
Re: In the figure above, if z = 50, then x + y = [#permalink]

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27 Dec 2012, 17:36
1
KUDOS
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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Joined: 26 Jun 2012
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Re: In the figure above, if z = 50, then x + y = [#permalink]

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18 Jun 2013, 23:50
3
KUDOS
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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Joined: 10 Oct 2012
Posts: 629
Re: In the figure above, if z = 50, then x + y = [#permalink]

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19 Jun 2013, 02:18
1
KUDOS
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.
Attachments

Angles.jpg [ 10.29 KiB | Viewed 12229 times ]

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Re: In the figure above, if z = 50, then x + y = [#permalink]

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29 Nov 2013, 13:17
1
KUDOS
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:

Intern
Joined: 04 Jun 2014
Posts: 49
Re: In the figure above, if z = 50, then x + y = [#permalink]

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25 Jul 2014, 00:06
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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 39751
Re: In the figure above, if z = 50, then x + y = [#permalink]

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25 Jul 2014, 03:09
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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In the figure above, if z = 50, then x + y = [#permalink]

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05 Nov 2015, 05:35
x + y = 360 - 90 (the right angle of the smaller triangle, which equals the other two angles of the smaller triangle). We don't need z to compute it
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Re: In the figure above, if z = 50, then x + y = [#permalink]

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13 Jul 2016, 07:50
Attachment:
Angles.png
In the figure above, if z = 50, then x + y =

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

When looking at the diagram, we want to start with the quadrilateral that contains angles z and y. We must remember that any quadrilateral has a total of 360 degrees. We know that two angles of the given quadrilateral are 90 degrees each and that z = 50 degrees. Thus, we can set up the following equation to determine the measure of angle y.

90 + 90 + 50 + y = 360

230 + y = 360

y = 130

Now that we know the value of angle y, we can move to the triangle in the lower part of the diagram. Let’s label it triangle ABC and draw it below. We see that angle ACB and angle y are supplementary, so angle ACB = 180 – 130 = 50 degrees. We also see that the triangle is a right triangle so the remaining angle, angle ABC = 180 – (90 + 50) = 40 degrees. Finally, since angle ABC and angle x are supplementary we see that angle x = 180 – 40 = 140 degrees.

Thus, x + y = 140 + 130 = 270.

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Re: In the figure above, if z = 50, then x + y =   [#permalink] 13 Jul 2016, 07:50
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