1. **State the problem:** We are given a circle with center $O$, a radius extending horizontally to the left, and an arc measuring $80^\circ$ from the end of this radius to a point on the circle. We need to find the value of the angle $x$ formed between the horizontal radius and the line segment to the point on the circle. 2. **Recall the circle angle rule:** The angle at the center of a circle subtended by an arc is equal to the measure of the arc itself. 3. **Apply the rule:** Since the arc measures $80^\circ$, the central angle $x$ subtended by this arc is also $80^\circ$. 4. **Conclusion:** Therefore, the value of $x$ is $$x = 80^\circ$$ This is because the angle at the center corresponding to an arc is equal to the arc's measure.