Chapter 9.6, Problem 4WE

To determine

ToFind: The measured of each numbered angle.

Answer to Problem 4WE

The value measured of each numbered of angle $\angle ACE\text{ is }65°.$

Explanation of Solution

Giveninformation:

  

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

Line $\overleftrightarrow{BZ}$ is tangent to point $\odot B$ .

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

An intercepted arc is equal to half of the measure of an inscribed angle.

So the value can be calculated as,

  $\begin{array}{l}\stackrel{⌢}{AE}=180°–\left(m\stackrel{⌢}{CD}+m\stackrel{⌢}{DE}\right)\hfill \\ =180°–\left(30°+20°\right)\hfill \\ =180°–50°\hfill \\ =130°\hfill \end{array}$

Further the value can be calculated as,

  $\begin{array}{l}\begin{array}{l}\angle ACE=\frac{1}{2}m\stackrel{⌢}{AE}\hfill \\ =\frac{1}{2}\times 130°\hfill \end{array}\\ =65°\end{array}$

Therefore the value measured of each numbered of angle $\angle ACE\text{ is }65°.$