To find the measure of arc EFC, we can use the fact that the entire circle measures 360 degrees. Since AE and FC are diameters, they split the circle into two semicircles.
Given that arc ED measures 17 degrees, we can determine the measure of arc EFC by considering the arc that complements it. The measure of arc EFC can be found by subtracting the measure of arc ED from the total angle of the semicircle.
The semicircle associated with diameter AE covers 180 degrees, therefore:
Measure of arc EFC = 180 degrees – Measure of arc ED
Measure of arc EFC = 180 degrees – 17 degrees = 163 degrees
Thus, the measure of arc EFC is 163 degrees.