Question

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

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Find the measure of arc DF

Since the inscribed angle $\angle DEF = 79^{\circ}$, by the inscribed - angle theorem, the measure of arc DF is $2\times79^{\circ}=158^{\circ}$.

Step3: Recall the property of the sum of arcs in a circle

The sum of the measures of the arcs of a circle is $360^{\circ}$. Given arc DE = $104^{\circ}$ and we want to find arc ECF. Let arc ECF be $x$. Then arc DE+arc DF + arc ECF=$360^{\circ}$.

Step4: Calculate the measure of arc ECF

We know arc DE = $104^{\circ}$ and arc DF = $158^{\circ}$. Substitute into the equation $104^{\circ}+158^{\circ}+x = 360^{\circ}$.
$x=360^{\circ}-(104^{\circ}+158^{\circ})$.
$x = 360^{\circ}-262^{\circ}=98^{\circ}$.

Answer:

$98^{\circ}$