Answer:
![\angle{C}=54](https://img.qammunity.org/2021/formulas/mathematics/high-school/sxfvlbkt1gpt8lfyf74urte28zdwymsw5v.png)
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://img.qammunity.org/2021/formulas/mathematics/high-school/6m8n2y6redkzxsu3z42o9gio2d2fq82rzh.png)
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://img.qammunity.org/2021/formulas/mathematics/high-school/742cogmljng5dkov4xj8vzn6zah4w0kvjd.png)
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://img.qammunity.org/2021/formulas/mathematics/high-school/4q7bmyqwo066yxehsc69hr5gvxn9004tvn.png)
Subtract the sum from 180:
![180-126=54](https://img.qammunity.org/2021/formulas/mathematics/high-school/3uyxma7rpbvgpaxr4l4v16nakx1y798wc5.png)
Therefore:
_
Check your work by adding the three identified angle measurements to see if they measure to 180°:
![59+67+54](https://img.qammunity.org/2021/formulas/mathematics/high-school/uahola8fc3x8vrjm0ngsp9hft10f928izl.png)
![=180](https://img.qammunity.org/2021/formulas/mathematics/college/wwdgpqkcm3smab3oii5rf2qibnd1c325b4.png)
The answer is correct!