what is the measure of arc ecf in circle g? 52° 98° 158° 177°
what is the measure of arc ecf in circle g? 52° 98° 158° 177°
Answer
Explanation:
Step1: Recall the arc - angle relationship
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 $EF$ is $2\times\angle EDF=2\times79^{\circ} = 158^{\circ}$.
Step2: Use the property of a circle
The sum of the measures of the arcs of a circle is $360^{\circ}$. We know that arc $ED = 104^{\circ}$ and we want to find arc $ECF$. The sum of arc $ED$, arc $EF$ and arc $FC$ is $360^{\circ}$. Arc $ECF$ is the sum of arc $EF$ and arc $FC$. Since the circle's total arc measure is $360^{\circ}$, and we know arc $ED = 104^{\circ}$ and arc $EF=158^{\circ}$, then arc $ECF=360^{\circ}- 104^{\circ}=158^{\circ}$.
Answer:
$158^{\circ}$