Miles had a piece of paper 1/4 of a large circle cut in three equal parts from the center point of the circle. What angle is the measure of each part?

The angle of 1/4 of a circle is given by:
 (1/4) * (360) = 90 degrees
 We now look for the angle that results from dividing 1/4 of a circle into three equal parts.
 We have then:
 (1/3) * (90) = 30 degrees.
 Answer:
 the measure of each part is:
 30 degrees