Answer:
arcEF = 66 degrees
Explanations:
The sum of angle at a point is 360 degrees. Taking the sum of all the measured arcs and equating to 360 will give;
[tex]arcDE+arcEF+arcFB+arcBC+arcCD=360^0[/tex]
Substitute the given angles
[tex]\begin{gathered} 82+arcEF+40+67+105=360 \\ arcEF+294=360 \end{gathered}[/tex]
Subtract 294 from both sides
[tex]\begin{gathered} arcEF+294-294=360-294 \\ arcEF=360-294 \\ arcEF=66^0 \end{gathered}[/tex]
Hence the measure of the arcEF is 66degrees
