Question

What is the value of x + y? How do you know? Show or explain work

Answer 1

The angle (2y - 5)° and 95° are vertical angles, then they are congruent, that is,

$2y-5=95$

Solving for y:

$\begin{gathered} 2y-5+5=95+5 \\ 2y=100 \\ \frac{2y}{2}=\frac{100}{2} \\ y=50 \end{gathered}$

The angle (3x + 55)° and 85° are vertical angles, then they are congruent, that is,

$3x+55=85$

Solving for x:

$\begin{gathered} 3x+55-55=85-55 \\ 3x=30 \\ \frac{3x}{3}=\frac{30}{3} \\ x=10 \end{gathered}$

Finally, the value of x + y is:

$x+y=10+50=60$