Question

what is the measure of minor arc ec? 17° 75° 149° 211°

Explanation:

Step1: Recall arc - central angle relationship

The measure of a minor arc is equal to the measure of its central angle.

Step2: Calculate the measure of central angle of arc $\overset{\frown}{EC}$

The sum of the central - angle measures around a point is $360^{\circ}$. But we can also find the measure of the central angle of arc $\overset{\frown}{EC}$ directly from the given angles. The central angle of arc $\overset{\frown}{EC}$ is the sum of the two given non - overlapping central angles. The two given angles are $83^{\circ}$ and $66^{\circ}$. So, the measure of the central angle of arc $\overset{\frown}{EC}$ is $83^{\circ}+66^{\circ}=149^{\circ}$.

Answer:

$149^{\circ}$