Question

Find the values of x and y.

Short answer

The value of x and y is 8 and 12 respectively.

Step-by-step solution

Step 1. Description of step.

If two parallel lines are intersected by a transversal then alternate interior angles are congruent. Therefore,

$$\begin{gathered} \left(2x+y\right)=\left(5x-y\right) \\ \begin{array}{c}5x-2x-y-y=0\\ 3x-2y=0\end{array} \end{gathered}$$

Step 2. Apply an angle sum theorem.

The sum of measures of all interior angles of a triangle is 180.

$$\begin{gathered} 100+2x+y+5x+y=180 \\ \begin{array}{c}7x+2y=180-100\\ 7x+2y=80\end{array} \end{gathered}$$

Step 3. Description of step.

Add equations obtained in step 1 and step 2 and simplify to find the value of x.

Step 4. Description of step.

Substitute 8 for $x$into $3x-2y=0$to find the value of y.

role="math" $\begin{array}{c}3\times 8-2y=0\\ 24-2y=0\end{array}$

role="math" localid="1638187017881" $\begin{array}{c}\frac{2y}{2}=\frac{24}{2}\\ y=12\end{array}$

Therefore, the value of x and y is 8 and 12 respectively.