# Lesson 14

Alternate Interior Angles

Let’s explore why some angles are always equal.

### Problem 1

Use the diagram to find the measure of each angle.

- \(m\angle ABC\)
- \(m\angle EBD\)
- \(m\angle ABE\)

### Problem 2

Lines \(k\) and \(\ell\) are parallel, and the measure of angle \(ABC\) is 19 degrees.

- Explain why the measure of angle \(ECF\) is 19 degrees. If you get stuck, consider translating line \(\ell\) by moving \(B\) to \(C\).
- What is the measure of angle \(BCD\)? Explain.

### Problem 3

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

### Problem 4

Lines \(s\) and \(t\) are parallel. Find the value of \(x\).

### Problem 5

The two figures are scaled copies of each other.

- What is the scale factor that takes Figure 1 to Figure 2?
- What is the scale factor that takes Figure 2 to Figure 1?