Chapter 9.6, Problem 1WE

To determine

To find: the measure of $\angle 1$ angle.

Answer to Problem 1WE

The value of angle $\angle 1$ 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 $\odot O$ .

  $marcBC=90$

Consider the fact that measure of an arc is defined to be the measure of its central angle.

A central angle of a circle is an angle with its vertex at the center of the circle.

Angle $\angle 1$ is a central angle and it measure is equal to the measure of an arc $marcBC$ .

Also from above $marcBC=90°$ .

Therefore, the value of angle $\angle 1$ is $90°$ .