The measure of arc EF = 41°
Step-by-step explanation:
Given:
Arc DE = 73°
![\angle FED=123\°](/tpl/images/0409/4995/45a22.png)
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,
![\textrm{Major Arc DGF}=2\times \angle FED\\\textrm{Major Arc DGF}=2\times 123\\\textrm{Major Arc DGF}=246\°](/tpl/images/0409/4995/d6883.png)
Now, we know that sum of all arcs on a circle is equal to 360°.
Therefore, arc DGF + arc DE + arc EF = 360°
![246+73+arc\ EF=360\\319+arc\ EF=360\\arc\ EF=360-319=41\°](/tpl/images/0409/4995/71b6d.png)
Therefore, the measure of the arc EF is 41°.