1. **Problem statement:** Given $\angle ABP = 76^\circ$, find the value of $y$ in the figure. 2. **Relevant concept:** In circle geometry, the angle formed outside the circle by two secants is half the difference of the intercepted arcs. 3. **Formula:** If $\angle ABP$ is an exterior angle formed by secants, then $$\angle ABP = \frac{1}{2} |\text{arc} AC - \text{arc} BC|$$ 4. **Given:** $\angle ABP = 76^\circ$, and inside the circle, angles $y$ and $104^\circ$ are related to arcs intercepted by these secants. 5. Since $y$ and $104^\circ$ are angles subtended by arcs, and $\angle ABP$ is exterior, we use the exterior angle theorem for circles: $$\angle ABP = y - 104^\circ$$ 6. Substitute $\angle ABP = 76^\circ$: $$76^\circ = y - 104^\circ$$ 7. Solve for $y$: $$y = 76^\circ + 104^\circ = 180^\circ$$ **Final answer:** $y = 180^\circ$ which corresponds to option A.