The measure of arc DF is requested given a circle with center O and points D, E, F...
Check the final answer first, then review the worked steps.
Problem
The measure of arc DF is requested given a circle with center O and points D, E, F on the circle. The angle FEO is 38 degrees.
Step-by-step solution
Since OE and OF are radii, triangle OFE is isosceles. Thus, angle OFE = angle FEO = 38 degrees. The angle FOE = 180 - (38 + 38) = 180 - 76 = 104 degrees. Angle DOE is a straight angle, so it measures 180 degrees. Angle DOF = 180 - angle FOE = 180 - 104 = 76 degrees. The measure of arc DF is equal to the measure of the central angle DOF.
Answer
$76^{\circ}$