Math Problem Statement

What’s the measure of angle ABE?

What is the measure of angle ABE?

Solution

The diagram shows two intersecting lines. Angle ABE\angle ABE refers to the angle formed between points AA, BB, and EE.

From the diagram, we know that:

  • ABC=40\angle ABC = 40^\circ (given in the image).
  • Since lines ABAB and BCBC appear to be straight, angles on a straight line add up to 180180^\circ.

Thus, to find ABE\angle ABE: ABE=180ABC=18040=140.\angle ABE = 180^\circ - \angle ABC = 180^\circ - 40^\circ = 140^\circ.

Therefore, the measure of ABE\angle ABE is 140140^\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 ABC\angle ABC were 5050^\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 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles on a Straight Line
Supplementary Angles

Formulas

Angles on a straight line sum up to 180 degrees

Theorems

Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8