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 \\ (2y)/(2)=(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 \\ (3x)/(3)=(30)/(3) \\ x=10 \end{gathered}`

Finally, the value of x + y is:

`x+y=10+50=60`