Chapter 9.6, Problem 6CE

To determine

To find: find the measure of numbered angle

Answer to Problem 6CE

The measure of angle $\angle$ 6 is $40°$

Explanation of Solution

Given information: we have given the figure of circle

  

We can see that the measure of two intercepted arc are

  $160°$ and $360°-\left(160°+120°\right)=360°-280°=80°$

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

  $\begin{array}{c}\angle 6=\frac{1}{2}\left(160°-80°\right)\\ =\frac{1}{2}\left(80°\right)\\ =40°\end{array}$

Therefore, the measure of the angle $\angle$ 6 is $40°$