Question

in circle a, measure of arc cfe is 240°. what is the measure of ∠ cae? 150° 120° 240° 60°

Explanation:

Step1: Recall the total degrees in a circle

A full circle has \( 360^\circ \).

Step2: Find the measure of arc \( CDE \) (or the minor arc \( CE \))

The measure of arc \( CFE \) is \( 240^\circ \). The remaining arc (minor arc \( CE \)) will be \( 360^\circ - 240^\circ = 120^\circ \).

Step3: Relate the central angle to the arc

The central angle \( \angle CAE \) intercepts arc \( CE \). The measure of a central angle is equal to the measure of its intercepted arc. So \( \angle CAE \) has the same measure as arc \( CE \).

Answer:

\( 120^\circ \) (corresponding to the option with \( 120^\circ \))