Chapter 9.6, Problem 2WE

To determine

To find: the measure of $\angle 2$ angle.

Answer to Problem 2WE

The value of angle $\angle 2$ is $90°$ .

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 $\odot O$ .

  $marcBC=90$

And,

  $marcAC=180°$

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

  $\begin{array}{c}\angle AEC=\frac{1}{2}marcAC\\ =\frac{1}{2}\times 180°\\ =90°\end{array}$

Therefore, the value of $\angle 2$ is $90°$ .