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The problem asks for the measure of angle \( ABE \), where the diagram shows two intersecting lines. Given that angle \( ABC \) is marked as \( 40^\circ \) and line \( AE \) extends through point \( B \), we can apply some geometric rules to solve this:

- The lines appear to form a pair of intersecting straight lines at point \( B \). 
- Angle \( ABE \) and angle \( ABC \) are **adjacent angles** on a straight line (they form a linear pair), meaning their sum must equal \( 180^\circ \) since they lie on a straight line.

To calculate the measure of angle \( ABE \):
\[
\text{Angle ABE} = 180^\circ - 40^\circ = 140^\circ
\]

Thus, the measure of angle \( ABE \) is \( \boxed{140^\circ} \).

Let me know if you'd like more details or have any further questions!

Here are 5 related questions:
1. What is the sum of angles around a point?
2. How can you determine the measure of a vertical angle?
3. What is a linear pair of angles, and what properties do they have?
4. How would you solve for an unknown angle in a triangle?
5. How are adjacent angles related on a straight line?

**Tip:** For intersecting lines, vertical angles are always congruent, and adjacent angles form a linear pair!

Solve for the measure of angle ABE, given angle ABC = 40°. This problem demonstrates key geometry concepts such as angles on a straight line, the linear pair theorem, and the sum of angles. Perfect for students in Grades 6-8.

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