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In the figure below, what is the relationship between x, y, a

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In the figure below, what is the relationship between x, y, a [#permalink] New post 26 May 2019, 01:10
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In the figure below, what is the relationship between x, y, and z?

Attachment:
#GREexcercise In the figure below, what is the relationship between.jpg
#GREexcercise In the figure below, what is the relationship between.jpg [ 13.94 KiB | Viewed 1225 times ]


[Reveal] Spoiler: OA
z = x + y


Math Review
Question: 3
Page: 259
Difficulty: medium

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Re: In the figure below, what is the relationship between x, y, a [#permalink] New post 17 Oct 2019, 07:09
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Carcass wrote:
In the figure below, what is the relationship between x, y, and z?

Attachment:
#GREexcercise In the figure below, what is the relationship between.jpg


[Reveal] Spoiler: OA
z = x + y


Math Review
Question: 3
Page: 259
Difficulty: medium


Here,

exterior angle = sum of the opposite interior angles

i.e \(\angle z = \angle y + \angle x\)
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Re: In the figure below, what is the relationship between x, y, a [#permalink] New post 18 Nov 2019, 22:03
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Carcass wrote:
In the figure below, what is the relationship between x, y, and z?

Attachment:
The attachment #GREexcercise In the figure below, what is the relationship between.jpg is no longer available


[Reveal] Spoiler: OA
z = x + y


Math Review
Question: 3
Page: 259
Difficulty: medium


In the triangle MNO,
x+y+a = 180
a = 180 - (x+y)
Now, NL is a straight line, so
a + z = 180
180 - (x+y) + z = 180
we get z = x+y
This is called the exterior angle theorem.
Edit - Removed the explanation from the image and moved to text
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triangle.jpg
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Last edited by uchihaitachi on 19 Nov 2019, 09:59, edited 1 time in total.
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Re: In the figure below, what is the relationship between x, y, a [#permalink] New post 19 Nov 2019, 06:56
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Thank for the on-point explanation.

However, it would be better to post the figure and then the explanation as text. It is not that difficult and it would be searchable by the other students.

Thank you.

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Re: In the figure below, what is the relationship between x, y, a [#permalink] New post 19 Nov 2019, 10:16
Let's c be the third angle of the triangle.
the sum of the interior angle of a triangle is equal to 180.
Thus, (x + y) + c = 180

On the other hand z + c = 180
We can conclude that z = x + y
Re: In the figure below, what is the relationship between x, y, a   [#permalink] 19 Nov 2019, 10:16
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