Answer: First option.
Step-by-step explanation:
You can idenfity in the figure that [tex]\angle FCE[/tex] is formed by two secants that intersect outside of the given circle.
It is important to remember that, by definition:
[tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}( Difference\ of\ intercepted\ Arcs)[/tex]
Knowing this, you can set up the following equation:
[tex]m\angle FCE=\frac{1}{2}(BD-FE)[/tex]
Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle [tex]\angle FCE[/tex].
This is:
[tex]m\angle FCE=\frac{1}{2}(112\°-38\°)\\\\m\angle FCE=37\°[/tex]
