Chapter 3.2, Problem 7WE

To determine

To find: the values of x and y .

Answer to Problem 7WE

  $x=60°$

  $y=61°$

Explanation of Solution

Given:

The diagram:

Concept Used:

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

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

Label the given figure as shown below:

Now, lines $\overline{AB}\parallel \overline{CD}$ and $\overline{BC}$ is a transversal, so by theorem 3-2,

  $\angle x\cong \angle ABC$ (Alternate interior angles)

That is,

  $m\angle x=m\angle ABC=60°$

Similarly, lines $\overline{AB}\parallel \overline{CD}$ and $\overline{AC}$ is a transversal, so by postulate 10,

  $\angle y\cong \angle CAB$ (Corresponding angles)

That is,

  $m\angle y=m\angle CAB=61°$