Question

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

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. The inscribed angle $\angle{EDF}$ intercepts arc $EF$. Given $\angle{EDF}=79^{\circ}$, then the measure of arc $EF = 2\times\angle{EDF}=2\times79^{\circ}=158^{\circ}$.

Step2: Use the fact that the sum of arcs in a circle is 360°

The measure of arc $DEF$ is given as $104^{\circ}$. Let the measure of arc $ECF$ be $x$. We know that the sum of the measures of arcs in a circle is $360^{\circ}$. So, $104^{\circ}+x = 360^{\circ}- 158^{\circ}$.

Step3: Solve for the measure of arc ECF

First, simplify the right - hand side: $360^{\circ}-158^{\circ}=202^{\circ}$. Then, $x=202^{\circ}-104^{\circ}=98^{\circ}$.

Answer:

$98^{\circ}$