Answer:
![\angle{C}=54](https://tex.z-dn.net/?f=%5Cangle%7BC%7D%3D54)
Step-by-step explanation:
Let's first start by establishing that when it comes to a reflection, side lengths and angle measurements remain the same. With that being said, let's identify our angle measurements:
![\angle{A=}\\\angle{B}= 67\\\angle{C}=\\\angle{A'}=59\\\angle{B'}=\\\angle{C'}=\\](https://tex.z-dn.net/?f=%5Cangle%7BA%3D%7D%5C%5C%5Cangle%7BB%7D%3D%2067%5C%5C%5Cangle%7BC%7D%3D%5C%5C%5Cangle%7BA%27%7D%3D59%5C%5C%5Cangle%7BB%27%7D%3D%5C%5C%5Cangle%7BC%27%7D%3D%5C%5C)
As mentioned earlier, angle measurements will remain the same, so we can go ahead and identify the values of
&
![\angle{A=59}\\\angle{B}= 67\\\angle{C}=\\\angle{A'}=59\\\angle{B'}=67\\\angle{C'}=\\](https://tex.z-dn.net/?f=%5Cangle%7BA%3D59%7D%5C%5C%5Cangle%7BB%7D%3D%2067%5C%5C%5Cangle%7BC%7D%3D%5C%5C%5Cangle%7BA%27%7D%3D59%5C%5C%5Cangle%7BB%27%7D%3D67%5C%5C%5Cangle%7BC%27%7D%3D%5C%5C)
The sum of the angles in a triangle will always be equal to 180°.
Add the two identified angles of the original figure.
![59+67=126](https://tex.z-dn.net/?f=59%2B67%3D126)
Subtract the sum from 180:
![180-126=54](https://tex.z-dn.net/?f=180-126%3D54)
Therefore:
_
Check your work by adding the three identified angle measurements to see if they measure to 180°:
![59+67+54](https://tex.z-dn.net/?f=59%2B67%2B54)
![=180](https://tex.z-dn.net/?f=%3D180)
The answer is correct!