Question

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in circle a, $m\widehat{cfe}$ is $240^\circ$.
what is the measure of $\angle cae$
$\bigcirc$ $60^\circ$
$\bigcirc$ $120^\circ$
$\bigcirc$ $270^\circ$
$\bigcirc$ $360^\circ$

Explanation:

Step1: Find remaining arc measure

The total degrees in a circle is $360^\circ$. Subtract the given arc measure:
$m\overset{\frown}{CDE} = 360^\circ - 240^\circ = 120^\circ$

Step2: Relate arc to central angle

The measure of a central angle equals its intercepted arc. $\angle CAE$ intercepts $\overset{\frown}{CDE}$.
$m\angle CAE = m\overset{\frown}{CDE}$

Answer:

120° (Option B. 120°)