1. **State the problem:** We are given a triangle with an internal point E on side BC. We know one angle is $46^\circ$ at vertex C and another angle $y^\circ$ at vertex B between segments AB and BE. We need to find the value of $y$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always $180^\circ$. 3. **Identify the angles in triangle ABC:** The angles at vertices A, B, and C add up to $180^\circ$. We know angle C is $46^\circ$ and angle B includes $y^\circ$ plus possibly other parts, but since $y^\circ$ is the angle at B between AB and BE, and E lies on BC, $y$ is the angle at B inside the triangle. 4. **Use the fact that angle at B plus angle at C plus angle at A equals $180^\circ$:** Let angle A be $a^\circ$. Then $$y + 46 + a = 180$$ 5. **Without additional information about angle A or other angles, we cannot find $y$ directly.** However, since E lies on BC, and $y$ is the angle between AB and BE, if BE is along BC, then $y$ is the angle between AB and BC at B. So $y$ is the angle at vertex B of triangle ABC. 6. **Therefore, the problem reduces to finding angle B in triangle ABC given angle C is $46^\circ$ and angle A is unknown.** Without angle A, we cannot find $y$. 7. **If the problem implies that angle A is a right angle or some other known value, we can proceed.** Since no other data is given, the best we can do is express $y$ in terms of angle A: $$y = 180 - 46 - a = 134 - a$$ **Final answer:** $y = 134 - a$ degrees, where $a$ is the measure of angle A in triangle ABC. If angle A is known, substitute to find $y$.