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The new image shows another set of parallel lines intersected by a transversal, creating several angles. The given angles and markings are:

1. \( \angle a \)
2. \( \angle b \)
3. \( \angle c \)
4. \( \angle 100^\circ \)

Using the properties of parallel lines and transversals, we can determine the values of the unknown angles. Here are the properties we'll use:

1. **Corresponding Angles**: If the two lines are parallel, corresponding angles are equal.
2. **Alternate Interior Angles**: If the two lines are parallel, alternate interior angles are equal.
3. **Alternate Exterior Angles**: If the two lines are parallel, alternate exterior angles are equal.
4. **Consecutive Interior Angles**: If the two lines are parallel, consecutive interior angles are supplementary (add up to \(180^\circ\)).

Using these properties:

1. \( \angle b \) is corresponding to the given \( 100^\circ \) angle. Therefore, \( \angle b = 100^\circ \).

2. \( \angle a \) is an alternate interior angle to the given \( 100^\circ \) angle. Therefore, \( \angle a = 100^\circ \).

3. \( \angle y \) (not marked explicitly but implied) is a consecutive interior angle with the given \( 100^\circ \) angle. Therefore, \( \angle y + 100^\circ = 180^\circ \). Solving for \( \angle y \):
   \[
   \angle y = 180^\circ - 100^\circ = 80^\circ
   \]

4. \( \angle c \) is an alternate exterior angle to the angle \( y \). Therefore, \( \angle c = 80^\circ \).

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

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How can we identify alternate interior angles in parallel lines and transversals?
2. What are the properties of corresponding angles, and how do they help in solving problems?
3. Can you explain the concept of alternate exterior angles with an example?
4. How do consecutive interior angles help in determining if lines are parallel?
5. What is the significance of supplementary angles in parallel lines and transversals?
6. How can we use transversals to prove that lines are parallel?
7. What are some real-life applications of parallel lines and transversals in engineering or architecture?
8. How would the angles change if the transversal intersected non-parallel lines?

**Tip:** Practice identifying and using different angle relationships to strengthen your understanding of parallel lines and transversals.

Explore the properties of parallel lines intersected by a transversal and learn how to solve angle problems. This page covers corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. Suitable for Grades 7-9.

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