# Lesson 12

Alternate Interior Angles

Let’s explore why some angles are always equal.

### Problem 1

Segments $$AB$$, $$EF$$, and $$CD$$ intersect at point $$C$$, and angle $$ACD$$ is a right angle. Find the value of $$g$$.

### Problem 2

$$M$$ is a point on line segment $$KL$$. $$NM$$ is a line segment. Select all the equations that represent the relationship between the measures of the angles in the figure.

A:

$$a=b$$

B:

$$a+b=90$$

C:

$$b=90-a$$

D:

$$a+b=180$$

E:

$$180-a=b$$

F:

$$180=b-a$$

### Problem 3

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 8.)

### Problem 4

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 5

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

### Problem 6

Lines $$s$$ and $$t$$ are parallel. Find the value of $$x$$.