Answer:
38°
Explanation:
You want the measure of arc ED in the diagram shown.
Complementary angles
Call the center of the circle point O. Angle AOB is complementary to the angle marked 52°. That means the measure of angle AOB is ...
∠AOB = 90° -52° = 38°
Vertical angles
Angle EOD is a vertical angle with respect to angle AOB, so is congruent to it. This means angle EOD is also 38°.
The measure of arc ED is the same as the measure of central angle EOD.
Arc ED is 38°.