Final answer:
The terminal side of an angle measuring 72π/4 radians lies in Quadrant I, as this simplifies to 18π radians, equivalent to 9 full revolutions, leaving the terminal side along the positive x-axis.
Step-by-step explanation:
To determine in which quadrant the terminal side of an angle measuring 72π/4 radians lies, we first simplify the angle's measure. Simplifying, we have 72π/4 = 18π. Recall that one full revolution (360°) equals 2π radians. Hence, 18π radians corresponds to 9 full circles (since 18π/2π = 9). After completing these circles, the angle will terminate in the same position as if it were just a 0° angle. Therefore, the terminal side of this angle will always end along the positive x-axis, which is in Quadrant I.