1. The problem states that the figure represents $\frac{1}{5}$ of a full circle, and we need to find the measure of the marked central angle. 2. Recall that a full circle measures $360^\circ$. 3. Since the sector is $\frac{1}{5}$ of the full circle, the central angle $\theta$ is given by the formula: $$\theta = \frac{1}{5} \times 360^\circ$$ 4. Calculate the angle: $$\theta = \frac{1}{5} \times 360^\circ = \cancel{\frac{1}{5}} \times 360^\circ = 72^\circ$$ 5. Therefore, the measure of the marked central angle is $72^\circ$.