1. **Problem:** What is an angle whose vertex is on a circle and whose sides contain chords of the circle? 2. **Definition:** An inscribed angle is an angle whose vertex lies on the circle and whose sides contain chords of the circle. 3. **Answer:** The correct choice is C. inscribed angle. 4. **Explanation:** The vertex of an inscribed angle is on the circle itself, and the sides of the angle are chords of the circle, which means they intersect the circle at two points each. 5. This distinguishes it from a central angle (vertex at the center), circumscribed angle (outside the circle), or vertical angle (formed by intersecting lines). Final answer: C. inscribed angle