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

Question

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.

chetan2u · Answer

Hi,
 z is equal to the SUM of two opposite interior angles.. 
ONE is opposite angle to x, so=x
The OTHER is complementary to 180, so = 180-y..

SO  z=x+180-y

C

MathRevolution · Answer

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.

michaelkalend · Answer

Can I please ask Bunuel to elaborate on the explanation? Thanks a lot in advance!

Bunuel · Answer

Solutions above are already clear enough. What exactly is confusing there? Please be more specific when asking a question. Thank you.

michaelkalend · Answer

I'm looking at the diagram, but can't get the point on how this one has derived - x+(180-z)+(180-y)=180

Bunuel · Answer

Three lines given form a triangle. x°, (180 - z)°, and (180 - y)° are the measures of this triangle's angles. The angles of a triangle always sum to 180º.

So, x° + (180 - z)° + (180 - y)° = 180º.

Hope it's clear.

santosh93 · Answer

As all the answers/explanations are revolving around the sum of angles in the triangle property, I would like to present the solution using different triangle property. I always good to know new approach in solving a problem because under test pressure we might not know which approach would strike the mind the quickest

Here's the triangle property which I used to solve the problem 
->  Exterior Angle = Sum of Interior Opposite angles

The exterior angle is "z".
And the interior opposite angles corresponding to "z" are 
 1."x"{obtained from opposite vertex angle} and 
 2."180-y" {straight line angle}

So by the law state above
 z = x + 180 -y
re-arranging the term to fit to options provided
 z = 180 -y +x

Hence answer is  C

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

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

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