Question

Find the values of $x$and $y$

Short answer

Values are$x=60°$and$y=61°$

Step-by-step solution

Step 1. Label the given figure

Step 2. Observations from figure

Arrowheads denote line segment $\overline{AB}$is parallel to$\overline{CD}$

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

- Find x degree

$\angle ABC$and $\angle x$forms a pair of alternate interior angles

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

$\begin{array}{c}\angle x\cong \angle ABC\\ m\angle x=m\angle ABC\end{array}$

Thus,$x°=60°$

- Find y degree

$\angle CAB$and $\angle y$forms a pair of corresponding angles

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

$\begin{array}{c}\angle y\cong \angle CAB\\ m\angle y=m\angle CAB\end{array}$

Thus,$y°=61°$