Home > CCG > Chapter 10 > Lesson 10.2.2 > Problem10-88

10-88.

Examine the diagram below. 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.

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

$23 + 48 + θ = 180º$
$θ = 109º$

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

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

$y = 71º$
$x = 109º$