Answer:
The measure of arc EF = 41°
Step-by-step explanation:
Given:
Arc DE = 73°
[tex]\angle FED=123\°[/tex]
Now, we know from central angle theorem that the measure of central angle by an arc is twice that of the angle made by the same arc at the circumference. Therefore,
[tex]\textrm{Major Arc DGF}=2\times \angle FED\\\textrm{Major Arc DGF}=2\times 123\\\textrm{Major Arc DGF}=246\°[/tex]
Now, we know that sum of all arcs on a circle is equal to 360°.
Therefore, arc DGF + arc DE + arc EF = 360°
[tex]246+73+arc\ EF=360\\319+arc\ EF=360\\arc\ EF=360-319=41\°[/tex]
Therefore, the measure of the arc EF is 41°.
