CPM Homework Help : CCG Problem 10-88

Examine the diagram at right. Use the given geometric relationships to solve for $x$ , $y$ , and $z$ . Be sure to justify your work by stating the geometric relationship and applicable theorem.

Hint:

Use the Triangle Angle Sum Theorem to find $x$ .

Step:

$23°+48°+θ=180°$
$θ=109°$

Angle labels added: intersection left & right, bottom labeled theta, intersection of left & fourth, exterior left labeled, alpha.

More Help:

Vertical angles are congruent. Use this information to find $x$ .

Hint 2:

$α+y=180°$
When solving for $α$ , remember that parallel lines have congruent corresponding angles.

Partial Answer:

$y=71°$
$x=109°$