1. **Problem statement:** Given a circle with center O and two chords forming two angles on the circumference, one angle is 100° and the other is $x^\circ$. We need to find the value of $x$. 2. **Key concept:** Angles subtended by the same chord or arc at the circumference of a circle are equal. 3. **Explanation:** Since the two angles 100° and $x^\circ$ are subtended by the same chord or arc, they are equal. 4. **Therefore:** $$x = 100$$ 5. **Answer:** The value of $x$ is 100°.