Direction: Find the value of each variable in a parallelogram.
[tex]\begin{gathered}\quad\quad\begin{gathered}\begin{array}{cc}\rm 1.) Finding \: the \: value \: of \: x \\ 8x - 3 = 2x + 9 \\ 8x - 2x = 9 + 3 & \\ 6x = 12 \\ \boxed{\pmb{x = 12}} \\ \\ \rm Finding \: the \: value \: of \: y \\ 3y - 5 = y + 5 & \\ 3y - y = 10 \\ 2y = 10 & \\ \boxed{\pmb{y = 5}} \end{array}\end{gathered}\end{gathered}[/tex]
[tex]\begin{gathered}\quad\begin{gathered}\begin{array}{cc} \rm 2.) Finding \: the \: value \: of \: x \\ (2x + 10) \degree + (5x - 5) \degree = 180 \degree \\ 7x = 180 \degree - 10 \degree + 5 \degree \\ 7x = 180 \degree - 5 \degree \\ 7x = 175 \degree \\ \rm x = \frac{175}{7} \\ \rm \boxed{\pmb{x = 25 \degree}} & \rm \\ \\ \rm Finding \: the \: value \: of \: y \\ (5x - 5) \degree + y = 180 \degree \\ y = 180 \degree - (5x - 5) \degree \\ y = 180 \degree - 120 \degree \\ \boxed{\pmb{y = 60 \degree}}\end{array}\end{gathered}\end{gathered} [/tex]
[tex]\begin{gathered}\quad\quad\begin{gathered}\begin{array}{cc} \rm 3.) Finding \: the \: value \: of \: x \\ 3x - 1 = 2x + 3 \\ 3x - 2x = 3 + 1 \\ x = 3 + 1 \\ \boxed{\pmb{x = 4}} \\ \rm \\ \rm Finding \: the \: value \: of \: y \\ 6y + 11 = 53 \\ 6y = 53 - 11 \\ 6y = 42 & \\ y = \frac{42}{6} \\ \boxed{\pmb{y = 7}} \end{array}\end{gathered}\end{gathered} [/tex]
