# 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.

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

### Problem 4

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 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 \(x\).