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# In the figure above, what is x + y in terms of z?

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Math Expert
Joined: 02 Sep 2009
Posts: 59628
In the figure above, what is x + y in terms of z?  [#permalink]

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24 Aug 2017, 01:59
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15% (low)

Question Stats:

88% (00:35) correct 13% (00:27) wrong based on 51 sessions

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In the figure above, what is x + y in terms of z?

(A) 180 – z
(B) 180 + z
(C) z – 180
(D) z + 180
(E) z

Attachment:

2017-08-24_1250.png [ 5.45 KiB | Viewed 2567 times ]

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Re: In the figure above, what is x + y in terms of z?  [#permalink]

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24 Aug 2017, 02:47
Bunuel wrote:

In the figure above, what is x + y in terms of z?

(A) 180 – z
(B) 180 + z
(C) z – 180
(D) z + 180
(E) z

Attachment:
2017-08-24_1250.png

z= 3rd internal angle of triangle.

Also x + y+ z =180
thus x+ y = 180-z

Ans A
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Posts: 3736
In the figure above, what is x + y in terms of z?  [#permalink]

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24 Aug 2017, 06:09
Bunuel wrote:

In the figure above, what is x + y in terms of z?

(A) 180 – z
(B) 180 + z
(C) z – 180
(D) z + 180
(E) z

Attachment:
2017-08-24_1250.png

1. Vertical angle

The unnamed angle inside the triangle and z are congruent vertical angles.

Sum of interior angles of a triangle = 180

x + y + z = 180

x + y = 180 - z

z is on the same line as an exterior angle of the triangle, call it w, whose measure equals the sum of non-adjacent interior angles x and y.

x + y = w
z + w = 180
Substitute:
z + x + y = 180
x + y = 180 - z

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Re: In the figure above, what is x + y in terms of z?  [#permalink]

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29 Aug 2017, 16:17
Bunuel wrote:

In the figure above, what is x + y in terms of z?

(A) 180 – z
(B) 180 + z
(C) z – 180
(D) z + 180
(E) z

Since the unmarked interior angle of the triangle is congruent with the angle measuring z degrees, it also measures z degrees. Since the sum of the three interior angles of a triangle is 180 degrees, we have:

x + y + z = 180

x + y = 180 - z

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Re: In the figure above, what is x + y in terms of z?   [#permalink] 29 Aug 2017, 16:17
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