Question

Find the values of $x$and $y$

Short answer

Values are$x=10$and$y=45$

Step-by-step solution

Step 1. Label the given figure

Step 2. Observations from figure

Arrowheads denotes line segment $\overline{AB}$is parallel to $\overline{DC}$

Line segments $\overline{BC}$and $\overline{AD}$are transversal to these parallel lines

Step 3. Find x degree

$\angle BAD$and $\angle ADC$forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$\begin{array}{c}m\angle BAD+m\angle ADC=180\\ 4x+14x=180\\ 18x=180\\ x=\frac{180}{18}\end{array}$

Thus,$x=10$

Step 4. Find y degree

$\angle DCB$and $\angle CBA$forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$\begin{array}{c}m\angle DCB+m\angle CBA=180\\ 2y+90=180\end{array}$

$\begin{array}{c}2y=180-90\\ y=\frac{90}{2}\end{array}$