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Manager  Joined: 02 Dec 2012
Posts: 173
In the figure above, if z = 50, then x + y =  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (01:23) correct 11% (01:42) wrong based on 1122 sessions

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Attachment: Angles.png [ 9.95 KiB | Viewed 30003 times ]
In the figure above, if z = 50, then x + y =

(A) 230
(B) 250
(C) 260
(D) 270
(E) 290
Intern  Joined: 26 Jun 2012
Posts: 24
Location: Germany
GMAT 1: 570 Q31 V39 GMAT 2: 710 Q43 V44 Re: In the figure above, if z = 50, then x + y =  [#permalink]

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5
1
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
General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
In the figure above, if z = 50, then x + y =  [#permalink]

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3
1
1 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 25172 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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Manager  Joined: 03 Nov 2009
Posts: 55
Re: In the figure above, if z = 50, then x + y =  [#permalink]

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1
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
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 590
Re: In the figure above, if z = 50, then x + y =  [#permalink]

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1
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 24475 times ]

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Joined: 14 Apr 2009
Posts: 2273
Location: New York, NY
Re: In the figure above, if z = 50, then x + y =  [#permalink]

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1
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: 46
Re: In the figure above, if z = 50, then x + y =  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 58445
Re: In the figure above, if z = 50, then x + y =  [#permalink]

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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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GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38 WE: Real Estate (Mutual Funds and Brokerage)
In the figure above, if z = 50, then x + y =  [#permalink]

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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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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.

The answer is D.
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Re: In the figure above, if z = 50, then x + y =  [#permalink]

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y= 360-(50+90+90)= 130 (straight line method and sum of angles of a quadrilateral is 360)

x is the exterior angle and hence = (180-y)+90= 140

140+130= 270

I did not use the parallel line method. Hope this is fine.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the figure above, if z = 50, then x + y =  [#permalink]

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Hi All,

This question requires an understanding of similar triangles, "line" rules (specifically that the angles on a line sum to 180 degrees) and that the angles in a triangle sum to 180 degrees.

We're told that Z=50. Since the two triangles have the same angles (they both have a 90 and the same angle "next" to angle X), we know that the triangles are similar. This means that Z and the angle "next" to Y are the SAME (meaning that they BOTH = 50).

By extension, Y + 50 = 180, so Y = 130.

The angles in the smaller triangle are 90, 50 and the missing angle. 90+50 = 140, so the missing angle = 40.

40 + X = 180, so X = 140

Thus, X+Y = 130+140 = 270

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

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_________________ Re: In the figure above, if z = 50, then x + y =   [#permalink] 07 May 2019, 03:25
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