In the given diagram, you are asked to determine the measure of angle $\angle ABE$ under the condition that $DE \parallel AB$.

Step-by-step explanation:

1. Parallel Line Concept: Since $DE \parallel AB$, and $\angle DGE$ (which is 94°) forms a transversal with these parallel lines, we can use the properties of parallel lines and angles.

2. Interior Angles: $\angle DGE$ and $\angle ABE$ are corresponding interior angles. Therefore, the measure of $\angle ABE$ will be: $\angle ABE = 180^\circ - \angle DGE = 180^\circ - 94^\circ = 86^\circ$

Thus, $\angle ABE = 86^\circ$.

Would you like any further explanation or details?

Follow-up questions:

1. What are the properties of corresponding angles in parallel lines?
2. How do parallel lines affect angle relationships in transversals?
3. Could we use any other theorems to solve this problem?
4. How are alternate interior angles useful in parallel line problems?
5. Why is it important that $DE \parallel AB$ is given?

Tip:

Always remember to check for parallel lines in geometry problems, as they provide crucial information for solving for unknown angles or sides.