1. **State the problem:** We are asked to determine whether the measure of an intercepted arc of an inscribed angle is one half the measure of the inscribed angle. 2. **Recall the theorem about inscribed angles:** The measure of an inscribed angle is actually one half the measure of its intercepted arc. In symbols, if $\theta$ is the inscribed angle and $m$ is the measure of the intercepted arc, then $$\theta = \frac{1}{2} m.$$ 3. **Analyze the given statement:** The user’s statement says the intercepted arc's measure is half the inscribed angle’s measure, i.e., $$m = \frac{1}{2} \theta.$$ 4. **Compare with the theorem:** The correct relation is the reverse: the angle is half the intercepted arc, not the other way around. The intercepted arc's measure is actually twice the inscribed angle's measure: $$m = 2 \theta.$$ 5. **Conclusion:** The user's statement is **false** because the measure of the intercepted arc is not half the inscribed angle's measure, but rather, the inscribed angle is half the arc's measure.