https://file.aiquickdraw.com/mathbot/file/1722911139596zdv91toy.jpg

In the diagram you provided, angles are formed by the intersection of two lines \( m \) and \( n \) with a transversal.

Two angles are supplementary if the sum of their measures is 180 degrees. In the context of this diagram, supplementary angles include:

1. **Adjacent angles on a straight line**:
   - \(\angle 1\) and \(\angle 2\)
   - \(\angle 2\) and \(\angle 4\)
   - \(\angle 3\) and \(\angle 4\)
   - \(\angle 5\) and \(\angle 6\)
   - \(\angle 6\) and \(\angle 8\)
   - \(\angle 7\) and \(\angle 8\)

2. **Angles on a straight line that are not adjacent** (they still sum up to 180 degrees because the straight line forms a 180-degree angle):
   - \(\angle 1\) and \(\angle 3\)
   - \(\angle 5\) and \(\angle 7\)

These pairs of angles are supplementary.

Would you like more details, or do you have any questions?

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Here are 8 related questions to explore:

1. What are vertical angles, and which angles in this diagram are vertical?
2. How can you determine if two angles are congruent in this diagram?
3. Which angles in the diagram are corresponding angles?
4. How do alternate interior angles relate in this diagram?
5. Are there any pairs of angles that are complementary in this diagram?
6. What can you infer about angles on the same side of the transversal?
7. How do you prove that two lines are parallel based on angles?
8. Which angles are equal if the lines \(m\) and \(n\) are parallel?

**Tip:** Remember, adjacent angles on a straight line are always supplementary. This is a fundamental property of angles formed by a straight line.

Explore the concept of supplementary angles in geometry with a detailed explanation and diagram. Learn which angles are supplementary in a given diagram formed by intersecting lines and a transversal. Suitable for Grades 7-9 students studying basic geometry concepts.

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