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;
![arcDE+arcEF+arcFB+arcBC+arcCD=360^0](https://img.qammunity.org/2023/formulas/mathematics/college/sk8cf5tsxwwpcto9r6pstm5n8y4onycakm.png)
Substitute the given angles
![\begin{gathered} 82+arcEF+40+67+105=360 \\ arcEF+294=360 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/j47f41lwjndge7nrd5n4kn2q8gz43a9dwi.png)
Subtract 294 from both sides
![\begin{gathered} arcEF+294-294=360-294 \\ arcEF=360-294 \\ arcEF=66^0 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/yhria9ar30qm0w5qkhtvqph89of0c9vebk.png)
Hence the measure of the arcEF is 66degrees