Question

PLEASE HELP ME PLEASE AND THANK

Answer 1

Answer: OPTION C.

Step-by-step explanation:

You can observe in the picture given in the exercise that  $\angle E$ is formed by two secants intersecting outside the circle.

It is necessary to remember that, by definition:

$Angle\ formed\ by\ two\ Secants=\frac{1}{2}(Difference\ of\ Intercepted\ Arcs)$

You can also identify that the Intercepted Arcs are the following:

$CD=110\°\\\\AB=30\°$

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  $\angle E$ , which is the angle formed by the intersection of the secants.

Therefore, you get:

$m\angle E=\frac{1}{2}(110\°-30\°)\\\\m\angle E=40\°$