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What is the value of z, in terms of y and x?

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by Max@Math Revolution » Sun May 15, 2016 8:20 pm
What is the value of z, in terms of y and x?
A. 180-x+y
B. 180-y-x
C. 180-y+x
D. x-y+90
E. y-x+90

*An answer will be posted in two days.
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by 800_or_bust » Mon May 16, 2016 8:43 am
Max@Math Revolution wrote:What is the value of z, in terms of y and x?
A. 180-x+y
B. 180-y-x
C. 180-y+x
D. x-y+90
E. y-x+90

*An answer will be posted in two days.
The three angles of the interior triangle can be expressed as x, 180-z, and 180-y, respectively. Since the sum of the angles of a triangle is 180, we can set up the following equation:

180 = x + 180 - z + 180 - y

Add z & subtract 180 from both sides of the equation...

z = x + 180 - y = 180 - y + x

Answer choice C
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by Max@Math Revolution » Tue May 17, 2016 3:06 pm
From the diagram above, we can see that x+(180-z)+(180-y)=180. Hence, x-z-y+180=0 and, thus, z=x-y+180. Thus, the correct answer is C.
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