# 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.

1. $$m\angle ABC$$
2. $$m\angle EBD$$
3. $$m\angle ABE$$
(From Unit 1, Lesson 9.)

### Problem 2

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

1. Explain why the measure of angle $$ECF$$ is 19 degrees. If you get stuck, consider translating line $$\ell$$ by moving $$B$$ to $$C$$.
2. 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.

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