Question

In the circle below

Answer 1

Angle FCE measures
`37^o`, which matches the first option listed among the list of possible answers.

Explanation:

Notice that we are in the present of what is considered a "secant-secant" angle, where the angle formed at vertex "C" (angle FCE) is given by "half of the difference between the larger arc subtended by the two secants, minus the smaller arc subtended."

Since in this cases the larger arc is arc BD (of measure
`112^o`), and the smaller arc is arc EF (of measure
`38^o`), then the formula for angle FCE gives:

`FCE = (1)/(2) (112^o-38^o)\\FCE= (74^o)/(2) \\FCE=37^o`, which agrees with the first option listed among possible solutions.