Chapter 9.6, Problem 8WE

To determine

To calculate: The measure of each numbered angle.

Answer to Problem 8WE

The value measure of each numbered angle = 60°.

Explanation of Solution

Given information:

  

Line $\overline{AC}$ is a diameter.

Line $\overleftrightarrow{BZ}$ is tangent to the point $\odot \text{O}$

  $\begin{array}{l}m\stackrel{⌢}{BC}=90\hfill \\ m\stackrel{⌢}{CD}=30\hfill \\ m\stackrel{⌢}{DE}=20\hfill \end{array}$

On the interaction of two chords inside circle, the formed angle is equal tohalf of sum of the intercepted arcs.

So the value of angle can be calculated as,

  $\begin{array}{l}m\angle 8=\frac{1}{2}\left(m\stackrel{⌢}{AB}-m\stackrel{⌢}{CD}\right)\hfill \\ =\frac{1}{2}\left(90+30\right)\hfill \\ =\frac{1}{2}\times 120\hfill \\ =60\hfill \end{array}$

Therefore, the value measure of each numbered angle = 60°.