Chapter 9.6, Problem 15WE

To determine

To find: find the value of $m\angle A$ =?

Answer to Problem 15WE

The value of $m\angle A=30$

Explanation of Solution

Given information: we have given $m\stackrel{⌢}{CT}=110$ , $m\stackrel{⌢}{BT}=50$ and the figure of circle

  

As we know

The measure of an angle formed by a secant and a tangent drawn from the point outside a circle is equal to half the difference of the measures of the intercepted arcs.

Therefore from given figure we must have

  $\begin{array}{c}m\angle A=\frac{1}{2}\left(m\stackrel{⌢}{CT}-m\stackrel{⌢}{BT}\right)\\ m\angle A=\frac{1}{2}\left(110-50\right)\\ m\angle A=\frac{60}{2}\\ m\angle A=30\end{array}$

Therefore, the value of $m\angle A=30$