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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]  26 May 2019, 01:10
Expert's post
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 [ 13.94 KiB | Viewed 3043 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]  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]  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 [ 11.37 KiB | Viewed 2484 times ]

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Last edited by uchihaitachi on 19 Nov 2019, 09:59, edited 1 time in total.
Founder
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Re: In the ﬁgure below, what is the relationship between x, y, a [#permalink]  19 Nov 2019, 06:56
Expert's post
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.

Regards
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Re: In the ﬁgure below, what is the relationship between x, y, a [#permalink]  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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