Question

Find the values of $x$and $\mathrm{y}$

Short answer

Values are $\mathit{x}\mathbf{=}\mathbf{60}$ and$\mathit{y}\mathbf{=}\mathbf{18}$

Step-by-step solution

Step 1. Label the given figure

Step 2. Observations from figure

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

Double arrowheads denotes line segment $\overline{HE}$is parallel to$\overline{FG}$

Line segment $\overline{HE}$is transversal to parallel lines $\overline{AB}$and$\overline{CD}$

Line segment $\overline{FD}$is transversal to parallel lines $\overline{HE}$and$\overline{FG}$.

Step 3. Find x degree

$\angle BAH$and $\angle BAE$forms a linear pair, so sum of these angles is supplementary

$m\angle BAH+m\angle BAE=180$

$120+m\angle BAE=180$

$m\angle BAE=180-120$

$m\angle BAE=60$

$\angle BAE$and $\angle DCE$forms a pair of corresponding angles

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