Chapter 9.7, Problem 6ST2

To determine

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

Answer to Problem 6ST2

The value of $m\angle FPE=35$ .

Explanation of Solution

Given information:

Given figure,

$\overline{PE}$ and $\overline{PF}$ are secants and $\overline{PJ}$ is a tangent.

If $marcEF=100$ and $marcGH=30$

Calculation:

The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from appoint outside a circle is equal to half the difference of the measures of the intercepted arcs.

Since, $\overline{PE}$ and $\overline{PF}$ are secants, therefore solve as follows,

  $\begin{array}{c}m\angle FPE=\frac{1}{2}\left(marcEF-marcGH\right)\\ =\frac{1}{2}\left(100-30\right)\\ =35\end{array}$

Therefore, the value of $m\angle FPE=35$ .