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The image shows two parallel lines intersected by a transversal, creating several angles. The given angles are:

1. \( \angle 1 \) is marked as \( 80^\circ \)
2. \( \angle a \)
3. \( \angle b \)
4. \( \angle c \)

We can use the properties of parallel lines and transversals to find the unknown angles. Here are some key properties:

1. **Corresponding Angles**: Angles in the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, corresponding angles are equal.
2. **Alternate Interior Angles**: Angles on opposite sides of the transversal but inside the two lines. If the two lines are parallel, alternate interior angles are equal.
3. **Alternate Exterior Angles**: Angles on opposite sides of the transversal but outside the two lines. If the two lines are parallel, alternate exterior angles are equal.
4. **Consecutive Interior Angles**: Angles on the same side of the transversal and inside the two lines. If the two lines are parallel, consecutive interior angles are supplementary (add up to \(180^\circ\)).

Using these properties:

1. \( \angle a \) is corresponding to the given \( 80^\circ \) angle. Therefore, \( \angle a = 80^\circ \).

2. \( \angle b \) is an alternate exterior angle to the given \( 80^\circ \) angle. Therefore, \( \angle b = 80^\circ \).

3. \( \angle c \) is a consecutive interior angle with the given \( 80^\circ \) angle. Therefore, \( \angle c + 80^\circ = 180^\circ \). Solving for \( \angle c \):
   \[
   \angle c = 180^\circ - 80^\circ = 100^\circ
   \]

In summary:
- \( \angle a = 80^\circ \)
- \( \angle b = 80^\circ \)
- \( \angle c = 100^\circ \)

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How do we identify corresponding angles in parallel lines and transversals?
2. What are alternate interior angles, and how do they relate to parallel lines?
3. Can you define alternate exterior angles and their properties with parallel lines?
4. How are consecutive interior angles used to identify parallel lines?
5. What is the sum of angles on a straight line, and how does it help in solving transversal problems?
6. How can you use the properties of transversals to prove lines are parallel?
7. Can you give an example of a real-world application of parallel lines and transversals?
8. How would the problem change if the lines were not parallel?

**Tip:** Always look for angle relationships like corresponding, alternate interior, and exterior angles when working with parallel lines and transversals.

Explore how to solve angle problems involving parallel lines and transversals. Learn about corresponding angles, alternate interior angles, and consecutive interior angles with clear explanations and examples. Suitable for Grades 7-9 students studying geometry.

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