1. **State the problem:** We need to find the measure of angle $\angle CAE$ given the angles $40^\circ$ and $104^\circ$ in a figure with two parallel lines and intersecting lines. 2. **Identify the relationships:** Since the lines are parallel, alternate interior angles and linear pairs apply. 3. **Use the linear pair rule:** The angle adjacent to $104^\circ$ on the straight line is $180^\circ - 104^\circ = 76^\circ$. 4. **Use the triangle angle sum:** The triangle formed at the vertex with angles $40^\circ$, $76^\circ$, and $\angle CAE$ must sum to $180^\circ$. 5. **Calculate $\angle CAE$:** $$\angle CAE = 180^\circ - 40^\circ - 76^\circ = 64^\circ$$ 6. **Conclusion:** The measure of $\angle CAE$ is $64^\circ$.