Question

Find the values of x and y. (image below)

Answer 1

Opposite angles have the same measures. This allows you to set and solve the following equations:

$\begin{cases} 26-6x = 20-8x \\ 5y = 9y-76 \end{cases}$

To solve both equations, let's move all the terms involving the variables on the left hand side, and all constant terms on the right hand side:

$\begin{cases} -6x+8x = 20-26 \\ 5y-9y = -76 \end{cases}$

Sum like terms:

$\begin{cases} 2x = -6 \\ -4y = -76 \end{cases}$

Divide the first equation by 2 and the second by -4:

$\begin{cases} x = -3 \\ y = 19 \end{cases}$