Chapter 9.6, Problem 5CE

To determine

To find: find the measure of numbered angle

Answer to Problem 5CE

The measure of angle $\angle$ 5 is $45°$

Explanation of Solution

Given information: we have given 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

  $\begin{array}{c}\angle 5=\frac{1}{2}\left(170°-80°\right)\\ =\frac{1}{2}\left(90°\right)\\ =45°\end{array}$

Therefore, the measure of the angle $\angle$ 5 is $45°$