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The diagram shows two intersecting lines. Angle \( \angle ABE \) refers to the angle formed between points \( A \), \( B \), and \( E \).

From the diagram, we know that:
- \( \angle ABC = 40^\circ \) (given in the image).
- Since lines \( AB \) and \( BC \) appear to be straight, angles on a straight line add up to \( 180^\circ \).

Thus, to find \( \angle ABE \):
\[
\angle ABE = 180^\circ - \angle ABC = 180^\circ - 40^\circ = 140^\circ.
\]

Therefore, the measure of \( \angle ABE \) is \( 140^\circ \).

Would you like more details or have any other questions?

Here are some related questions for deeper understanding:
1. What are adjacent angles, and how do they relate to this problem?
2. How do supplementary angles apply to angles on a straight line?
3. Can you identify any vertical angles in the diagram?
4. How would the answer change if \( \angle ABC \) were \( 50^\circ \)?
5. What is the difference between interior and exterior angles in geometry?

**Tip:** Always remember that angles on a straight line sum up to \( 180^\circ \).

Learn how to find the measure of angle ABE in a geometry problem using the supplementary angles theorem. Given that angle ABC is 40 degrees, this solution guides you through calculating the complementary angle on a straight line. Suitable for students in Grades 6-8.

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