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What should the measure of angle 1 be? Explain

To determine the measure of \(\angle 1\) so that line \(c\) is parallel to line \(b\), we'll use the properties of parallel lines and angles formed by a transversal.

### Step 1: Analyze the Diagram
- Lines \(a\) and \(b\) intersect at a point, forming angles on the poster board.
- Line \(c\) is to be drawn such that it is parallel to line \(b\).
- The angle adjacent to \(\angle 1\) is given as \(75^\circ\).

### Step 2: Use the Corresponding Angles Postulate
For line \(c\) to be parallel to line \(b\), \(\angle 1\) and the angle that is formed at the intersection of line \(a\) and \(b\) must be corresponding angles.

Corresponding angles are equal when the lines are parallel. Therefore, \(\angle 1\) must be equal to the given angle \(75^\circ\) since it is the corresponding angle to the \(75^\circ\) angle formed at the intersection of lines \(a\) and \(b\).

### Step 3: Conclusion
\[
\text{Measure of } \angle 1 = 75^\circ
\]
This ensures that line \(c\) is parallel to line \(b\), according to the **Corresponding Angles Postulate**.

Would you like more details or have any questions?

Here are some related questions:

1. What is the Alternate Interior Angles Theorem, and how does it apply here?
2. How would the measure of \(\angle 1\) change if line \(c\) were perpendicular to line \(b\)?
3. What is the difference between corresponding angles and alternate interior angles?
4. How would you verify that line \(c\) is parallel to line \(b\) after drawing it?
5. Can the Corresponding Angles Postulate be applied to other geometric shapes like triangles?

**Tip:** Always look for relationships between angles when working with parallel lines and a transversal; this will help you determine the necessary measurements easily.

Explore how to determine the measure of angle 1 so that line c is parallel to line b using the Corresponding Angles Postulate. Understand the properties of parallel lines and transversals in geometry. Suitable for students in Grades 6-8.

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