Question

Choose the correct word to fill in the blank.

In circle C below, ∠FCE is a(n) _______.



central angle

major arc

inscribed angle

minor arc

Answer 1

central angle

Explanation:

You want a description of angle FCE in circle C.

Naming

A circle is named by its center. Circle C has its center at point C.

An angle is named with the vertex point in the middle of the name. Angle FCE has its vertex at point C, which we already know is the center of the circle.

Central angle

A central angle is one that has its vertex at the center of the circle. Its defining rays intersect the circle. Here those intercept points are E and F.

In circle C, angle FCE is a central angle.

__

Additional comment

Angle DAB has its vertex on the circle, and its rays intercept an arc of the circle. Angle DAB is an "inscribed angle."

The arc EF that is labeled 145° is less than 180°, so is a "minor arc." The major arc is usually named including another point on the arc, so we have arc EBF as a "major arc." Its measure is 215°, which is more than 180°.