The angle (2y - 5)° and 95° are vertical angles, then they are congruent, that is,
[tex]2y-5=95[/tex]
Solving for y:
[tex]\begin{gathered} 2y-5+5=95+5 \\ 2y=100 \\ \frac{2y}{2}=\frac{100}{2} \\ y=50 \end{gathered}[/tex]
The angle (3x + 55)° and 85° are vertical angles, then they are congruent, that is,
[tex]3x+55=85[/tex]
Solving for x:
[tex]\begin{gathered} 3x+55-55=85-55 \\ 3x=30 \\ \frac{3x}{3}=\frac{30}{3} \\ x=10 \end{gathered}[/tex]
Finally, the value of x + y is:
[tex]x+y=10+50=60[/tex]
