Chapter 9.6, Problem 20WE

To determine

The value of $m\angle P$

Answer to Problem 20WE

The value of $m\angle P=180-t$

Explanation of Solution

Given information:

It is given $m\stackrel{⌢}{XY}=t$ and the figure of circle

  

Given $m\stackrel{⌢}{XY}=t$

Therefore, $m\stackrel{⌢}{XZY}=360-t$

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

  $\begin{array}{c}m\angle P=\frac{1}{2}\left(m\stackrel{⌢}{XZY}-m\stackrel{⌢}{XY}\right)\\ =\frac{1}{2}\left\{\left(360-t\right)-t\right\}\\ =\frac{1}{2}\left(360-2t\right)\\ =180-t\end{array}$

Therefore, the value of $m\angle P=180-t$