CPM Homework Help : CCG Problem 5-53

Use the relationships found in each of the diagrams below to solve for $x$ and $y$ . Assume the diagrams are not drawn to scale. State which geometric relationships you used.

Hint 1(a):
Solve for the missing angle in the triangle with $70º$ and $41º$ . Use the Triangle Angle Sum Theorem to solve for the missing angle.
Step 1(a):
$41º+70º+\text{missing angle}=180º$
$\text{missing angle}=69º$
Hint 2(a):
$y$ and the $69º$ angle are supplementary angles, because they form a linear pair.
Step 2(a):
$69º+y=180º$
$y=111º$
Hint 3(a):
The $69º$ angle and the angle across from it are vertical angles and vertical angles are congruent.
Step 3(a):
Using the Triangle Angle Sum Theorem and the triangle on the right, $69º+58º+x=180º$ so $x=53º$

Answer (b):
$y=79º$ , $x=47º$

Hint (c):
Find the measures of any angles that may relate to the unknown angles by using the angles given.

Hint (d):
This is a special right triangle. Try drawing it to scale and then solve for $x$ and $y$ .