CPM Homework Help : GC Problem 10-71

Examine the diagram at right. Use the given geometric relationships to solve for $x, y,\text{ and }z$ . 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:

$23º+48º+θ=180º$
$θ = 109º$

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:

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

Partial Answer:

$y = 71º$
$x = 109º$