What if you were given two angles of unknown size and were told they are vertical angles? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of vertical angles to solve problems like this one.

### Watch This

Watch the first part of this video.

James Sousa: Angle Relationships

Then watch the third part of this video.

James Sousa: Complementary Angles

### Guidance

**
Vertical angles
**
are two non-adjacent angles formed by intersecting lines.
and
are vertical angles and
and
are vertical angles.

The
**
Vertical Angles Theorem
**
states that if two angles are vertical angles, then they are congruent.

#### Example A

Find .

is vertical angles with , so .

#### Example B

If and are vertical angles and and , what is the measure of each angle?

Vertical angles are congruent, so set the angles equal to each other and solve for . Then go back to find the measure of each angle.

So,

#### Example C

True or false: vertical angles are always less than .

This is false, you can have vertical angles that are more than . Vertical angles are less than .

### Guided Practice

Find the value of or .

1.

2.

3.

**
Answers:
**

1. Vertical angles are congruent, so set the angles equal to each other and solve for .

2. Vertical angles are congruent, so set the angles equal to each other and solve for .

3. Vertical angles are congruent, so set the angles equal to each other and solve for .

### Practice

Use the diagram below for exercises 1-2. Note that .

- Name one pair of vertical angles.

- If , find .

For exercise 3, determine if the statement is true or false.

- Vertical angles have the same vertex.

- If and are vertical angles and and , what is the measure of each angle?
- If and are vertical angles and and , what is the measure of each angle?
- If and are vertical angles and and , what is the measure of each angle?
- If and are vertical angles and and , what is the measure of each angle?
- If and are vertical angles and and , what is the measure of each angle?
- If and are vertical angles and and , what is the measure of each angle?
- If and are vertical angles and and , what is the measure of each angle?