Chapter 9.6, Problem 3WE

To determine

To find: the measure of $\angle 3$ angle.

Answer to Problem 3WE

The value of angle $\angle 3$ is $25°$ .

Explanation of Solution

Given information:

Given figure,

$\overleftrightarrow{BZ}$ is tangent to $\odot O$ ; $\overline{AC}$ is a diameter; $marcBC=90$ ; $marcCD=30,marcDE=20$ .

Calculation:

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

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

  $\begin{array}{l}marcBC=90°\\ marcCD=30°\\ marcDE=20°\end{array}$

Consider the fact that measure of an inscribed angle is equal to half the measure of its intercepted arc.

So the value can be calculated as,

  $\begin{array}{c}\angle EAC=\frac{1}{2}\left(marcCD+marcDE\right)\\ =\frac{1}{2}\left(30°+20°\right)\\ =25°\end{array}$

Therefore, the value of $\angle 3$ is $25°$ .