Question

what is the measure of arc ecf in circle g? 52° 158° 177° 98°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Angle $\angle{EDF}$ is an inscribed angle and its measure is $79^{\circ}$. The arc it intercepts is arc $ECF$.

Step2: Calculate arc ECF

By the inscribed - angle theorem, if $\theta$ is the measure of the inscribed angle and $s$ is the measure of the intercepted arc, then $\theta=\frac{s}{2}$. Given $\theta = 79^{\circ}$, we can solve for $s$. So, $s = 2\theta$. Substituting $\theta = 79^{\circ}$, we get $s=2\times79^{\circ}=158^{\circ}$.

Answer:

$158^{\circ}$