Chapter 11.5, Problem 39SPR

To determine

To find: The value of $m\angle 6$ .

Answer to Problem 39SPR

The required value of the angle is $142.5°$ .

Explanation of Solution

Given:

The given Figure is shown in Figure 1.

  

Figure 1

Calculation:

Consider that when the two secants or chord intersect inside the circle than each angle measure is the half the sum of the measure of its intercepted arcs.

Then,

  $\begin{array}{c}m\angle 6=\frac{1}{2}\left(360-40-35\right)\\ =\frac{1}{2}\left(285\right)\\ =142.5°\end{array}$