Solution:
Given:
[tex]\begin{gathered} m\angle DEF=64^0 \\ measure\text{ of }arc\text{ DF }=x \end{gathered}[/tex]Using the circle theorem, the angle subtended by an arc at the center is twice the angle subtended at the circumference.
It follows that;
[tex]\begin{gathered} angle\text{ at the center}=x \\ angle\text{ at the circumference}=64^0 \\ \\ Hence, \\ x=2\times64 \\ x=128^0 \end{gathered}[/tex]Therefore, the measure of arc DF is 128 degrees.
