Answer: OPTION C.
Step-by-step explanation:
You can observe in the picture given in the exercise that [tex]\angle E[/tex] is formed by two secants intersecting outside the circle.
It is necessary to remember that, by definition:
[tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}(Difference\ of\ Intercepted\ Arcs)[/tex]
You can also identify that the Intercepted Arcs are the following:
[tex]CD=110\°\\\\AB=30\°[/tex]
Then, knowing the measures of the Intercepted Arcs, you can substitute them into the equation shown before and then evaluate, in order to calculate the measure of [tex]\angle E[/tex] , which is the angle formed by the intersection of the secants.
Therefore, you get:
[tex]m\angle E=\frac{1}{2}(110\°-30\°)\\\\m\angle E=40\°[/tex]
