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In the figure above, what is x + y in terms of z?
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24 Aug 2017, 01:59
24 Aug 2017, 01:59
Expert Reply
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A
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D
E
Difficulty:
5%
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Question Stats:
90% (00:34) correct
10%
(00:27)
wrong
based on 59
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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 5676 times ]
Re: In the figure above, what is x + y in terms of z?
[#permalink]
24 Aug 2017, 02:47
24 Aug 2017, 02:47
Bunuel
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
In the figure above, what is x + y in terms of z?
[#permalink]
24 Aug 2017, 06:09
24 Aug 2017, 06:09
Expert Reply
Bunuel
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
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
2. Adjacent to exterior angle
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
Answer A
