### Home > CCG > Chapter 11 > Lesson 11.1.1 > Problem11-11

11-11.

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.

1. $\widehat{ABD} = 180º$ 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: $2x = 180º - 106º$

1. Which angles are supplementary? This will help you write equations to solve for $x$ and $y$.

1. Use the Law of Sines.

$x = 7.9$, $y = 7.2$

1. Use the Triangle Angle Sum Theorem.