Question

For the following figure, (a) state a theorem that allows you to conclude that $3x-7=11$(b) Find the values of $x$and$y$.

Short answer

a.The theorem state that if three parallel lines cut of a congruent segment on a transversal then they cut of a congruent segment on every transversal.

b. The values are $x=6,y=19$.

Step-by-step solution

a.Step 1- Check the figure.

Consider the figure.

Step 2- Step description.

Here from the figure, there are four parallel lines.

Thus,if three parallel lines cut of a congruent segment on a transversal then they cut of the congruent segment on every transversal.

Step 3- Step description.

Therefore, the theorem states thatif three parallel lines cut of the congruent segment on a transversal then they cut of a congruent segment on every transversal.

b.Step 1- Check the figure.

Consider the figure.

Step 2- Step description.

Use theorem which states that if three parallel lines cut of the congruent segment on a transversal then they cut of the congruent segment on every transversal.

Corresponding alternate exterior angles are congruent.

Thus, simplify the equations as follows:

$\begin{array}{c}3x-7=11\\ 3x=11+7\\ 3x=18\\ x=6\end{array}$

Step 3- Step description.

Similarly, simplify the equation as follows:

$\begin{array}{c}5x-y=11\\ 5\left(6\right)-y=11\\ 30-y=11\\ -y=11-30\\ y=19\end{array}$

Thus, the values are $x=6,y=19$.