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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]

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

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New post 27 Dec 2012, 07:19
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Image
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 19903 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]

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New post 27 Dec 2012, 17:36
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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]

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New post 18 Jun 2013, 23:50
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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.

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

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New post 19 Jun 2013, 02:18
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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]

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New post 29 Nov 2013, 13:17
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:

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

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

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New post 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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New post 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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New post 13 Jul 2016, 07:50
Walkabout wrote:
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.

Image

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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New post 04 Sep 2017, 04:18
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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Re: In the figure above, if z = 50, then x + y = [#permalink]

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New post 01 Feb 2018, 13:10
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] 01 Feb 2018, 13:10
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