Triangle \(ABC\) is similar to triangle \(XYZ\), where \(A\) and \(B\…

Question

Prompt

Triangle

A B C

is similar to triangle

X Y Z

, where

A

and

B

correspond to

X

and

Y

, respectively. The length of each side of triangle

X Y Z

k

times the length of its corresponding side in triangle

A B C

, where

k

is an integer greater than

1

. The measure, in degrees, of angle

Z

can be represented by the expression

9 x + 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

9 x + 29

k (9 x + 29)

90 - (9 x + 29)

180 - k (9 x + 29)