# 8.6: Corresponding Angles

**At Grade**Created by: CK-12

**Practice**Corresponding Angles

Malik is following an old map of the downtown area. He decides to draw his own map and label his favorite places so that he doesn't forget where to stop when he visits the city again. He notices that the original map looks like a lot of parallel and perpendicular lines with other lines as well. He wonders if he can figure out the angle for areas that are in similar positions in reference to the lines. He notices that his current corner looks similar to the next corner. In fact, the two streets appear to be parallel with a line connecting them. If the angle of one corner is

In this concept, you will learn how to identify and use corresponding angles.

### Identifying and Using Corresponding Angles

When a line intersects with two lines that are parallel, it forms the same angles of intersection with the first parallel line and the second. Let’s see what this looks like.

Notice that new angle relationships are formed and take note of the measures of each angle.

When line

In this situation, there is another angle relationship that will help us find the measure of the angles formed at either point of intersection. Every angle at the first intersection (between lines

Angle **corresponding angles .** Corresponding angles are in the same place in each intersection and have the same measure. Angles

Let’s look at an example.

What angle corresponds to angle

This time the parallel lines are vertical, but the relationships stay the same.

Angle

### Examples

#### Example 1

Earlier, you were given a problem about Malik and his map.

Malik wants to recreate the map so that only his favorite places are included. He is standing at the corner of a street that runs parallel to the next street and is intersected by the third street. If the angle of his current corner is

First, identify the location of the corners.

The corner is at an intersection of two streets and the next corner is at a parallel intersection.

Next, name the relationship between the angles of the two corners.

The corners have corresponding angles.

Then, name the measure of the next corner's angle.

The answer is that the angle measure of the next corner will be

#### Example 2

Solve the following problem.

In the figure above, the

First, identify the angle that corresponds to angle

The

Next, remember the relationship between corresponding angles.

Corresponding angles are equal.

Then, state the value of angle

Angle

The answer is that the measure of angle

#### Example 3

What is the measure of angle

First, identify the angle that corresponds to angle

The

Next, remember the relationship between corresponding angles.

Corresponding angles are equal.

Then, state the value of angle

Angle

The answer is that the measure of angle

#### Example 4

What angle corresponds to angle

First, identify the location of the angle.

Angle

Next, identify the location of the corresponding angle.

The corresponding angle will be the top left angle formed at the second intersection.

Then, name the corresponding angle.

The corresponding angle is angle

The answer is that angle

#### Example 5

What is the value of angle 5?

First, identify the angle that corresponds to angle 5.

Angle 5 corresponds with the given

Next, remember the relationship between corresponding angles.

Corresponding angles are equal.

Then, state the value of angle 5.

Angle 5 is

The answer is that the measure of angle 5 is

### Review

Define each term.

- Adjacent Angles
- Vertical Angles
- Parallel lines
- Perpendicular lines
- Supplementary angles
- Complementary angles
- Corresponding angles.

Use this diagram to answer the following questions.

- Are angles D and F vertical angles or corresponding angles?
- One angle that corresponds to angle D is ?
- An angle that corresponds to angle E is?
- True or false. Angle E and angle Q are corresponding angles?
- True or false. Angle E and angle S are corresponding angles?
- True or false. Angle E and angle Q are adjacent angles?
- How many pairs of vertical angles are there in this diagram?
- Can you find corresponding angles if the intersected lines are not parallel?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.6.

### Resources

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Adjacent Angles

Two angles are adjacent if they share a side and vertex. The word 'adjacent' means 'beside' or 'next-to'.Corresponding Angles

Corresponding angles are two angles that are in the same position with respect to the transversal, but on different lines.Intersecting lines

Intersecting lines are lines that cross or meet at some point.Parallel

Two or more lines are parallel when they lie in the same plane and never intersect. These lines will always have the same slope.Perpendicular lines

Perpendicular lines are lines that intersect at a angle.Supplementary angles

Supplementary angles are two angles whose sum is 180 degrees.Vertical Angles

Vertical angles are a pair of opposite angles created by intersecting lines.### Image Attributions

In this concept, you will learn how to identify and use corresponding angles.

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