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. \(m\angle ABE\)
Two lines, line E C and line A D, that intersect at point B. Angle C B D is labeled 45 degrees.
(From Unit 1, Lesson 9.)

Problem 2

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

Two parallel lines, k and l, cut by transversal line m.
  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.

Two lines that do not intersect. A third line intersects with both lines.

Find the missing angle measures marked with question marks.

Problem 4

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

Four lines. Two parallel lines are labeled s and t. Two other lines that intersect at a right angle at a point on line t. One angle is labeled 40 degrees. Another angle is labeled x degrees.

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?
Two identical quadrilaterals on a grid.