CPM Homework Help : GC Problem 11-10

For each of the relationships represented in the diagrams below, write and solve an equation for $x$ and/or $y$ . Justify your method. In part (a), assume that $C$ is the center of the circle.

Solution (a):
$\widehat{ABD} = 180º$ because $AD$ is a diameter
$\widehat{AB} + \widehat{BD} = \widehat{ABD}$
$106º + BD = 180º$
$BD=74º$
The intercepted arc is twice the inscribed angle
$BD = 2(x)\\ \ \ 74 = 2x\\ \quad x=371°$
One equation could be: $2x = 180º - 106º$

Hint (b):
Which angles are supplementary? This will help you write equations to solve for $x$ and $y$ .

Hint (c):
Use the Law of Sines.
Answer (c):
$x = 7.9$ , $y = 7.2$

Hint (d):
Use the Triangle Angle Sum Theorem.