To solve that question we must remember that the sum of all internal angles of a triangle is 180°, we can say that
[tex]\angle X+\angle Y+\angle Z=180[/tex]
That's a rule! it's always true.
The problem says that
[tex]\angle X+\angle Y=55[/tex]
Then let's use it in our equation!
[tex]\begin{gathered} \operatorname{\angle}X+\operatorname{\angle}Y+\operatorname{\angle}Z=180 \\ \\ 55+\operatorname{\angle}Z=180 \end{gathered}[/tex]
Now we can solve it for Z
[tex]\begin{gathered} 55+\angle Z=180 \\ \\ \angle Z=180-55 \\ \\ \angle Z=125° \end{gathered}[/tex]
Therefore the measure of Z is 125°
