Chapter 9.7, Problem 1ST2

To determine

To find: the value of $m\angle A$ .

Answer to Problem 1ST2

The value of $m\angle A=40$ .

Explanation of Solution

Given information:

Given figure,

  $\overleftrightarrow{MD}$ is tangent to the circle.

If $marcBD=80$

Calculation:

The measure of an inscribed angle is equal to half the measure of its intercepted arc. Therefore,

  $\begin{array}{c}m\angle A=\frac{1}{2}marcBD\\ =\frac{1}{2}\cdot 80\\ =40\end{array}$

Therefore, the value of $m\angle A=40$ .