Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem12-114

12-114.

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. $\widehat{ABD} = 180° (\text{because AD is a diameter)}$

$\widehat{AB} + \widehat{BD} = \widehat{ABD}$

$106° + BD = 180°$

$BD = 74°$

$\text{The intercepted arc is twice the inscribed angle}$

$BD = 2(x)$
$74 = 2x$
$x = 37°$

$\text{One equation could be: } 2x = 180° - 106°$

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