Question

What values must x and y have to make the quadrilateral a parallelogram?

Short answer

The values that must x and y must have to make the quadrilateral a parallelogram are 18 and 14 respectively.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Find the value of x.

As the sum of the adjacent angles of the parallelogram is $180°$.

Therefore, to make the given quadrilateral a parallelogram, the sum of the adjacent angles measuring $\left(8x-6\right)°$and$42°$ should be $180°$.

Therefore, the value of x can be obtained as:

$\begin{array}{c}8x-6+42=180\\ 8x+36=180\\ 8x=180-36\\ 8x=144\\ x=\frac{144}{8}\\ x=18\end{array}$

Therefore, the value of x is 18.

Step 3. Find the value of y.

As the opposite angles of the parallelogram are congruent.

Therefore, to make the given quadrilateral a parallelogram, the opposite angles measuring $\left(3y\right)°$and$42°$ should be equal.

Therefore, the value of y can be obtained as:

$\begin{array}{c}3y=42\\ y=\frac{42}{3}\\ y=14\end{array}$

Therefore, the value of y is 14.