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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

Triangle $ABC$ is similar to triangle $XYZ$, where $A$ and $B$ correspond to $X$ and $Y$, respectively. The length of each side of triangle $XYZ$ is $k$ times the length of its corresponding side in triangle $ABC$, where $k$ is an integer greater than $1$. The measure, in degrees, of angle $Z$ can be represented by the expression $9x+29$, where $x$ is an integer. Which of the following expressions represents the measure, in degrees, of angle $C$ for all possible values of $x$?

A

$9x+29$

B

$k(9x+29)$

C

$90-(9x+29)$

D

$180-k(9x+29)$