Vertical Angles: Definition, Examples, Chart, and Practice

What are vertical angles?

Vertical angles are the opposite angles made when two straight lines cross.

They do not sit next to each other. They face each other across the crossing point.

Vertical angles always have the same measure. If one vertical angle is 64°, the angle opposite it is also 64°.

Vertical angles rule

Use this rule when two lines cross.

Opposite angles are vertical angles. Vertical angles are equal.

This means you can copy the measure across the vertex from one angle to its opposite angle.

Vertical angles chart

This chart shows the two important relationships in a crossing-lines diagram.

Opposite angles are equal. Angles that sit next to each other on a straight line add to 180°, just like supplementary angles.

How to identify vertical angles

Step 1: Look for two lines that cross.

Step 2: Find the angle across from the angle you know.

Step 3: If the two angles are opposite and share only the crossing point, they are vertical angles.

Do not choose the angle beside it. The angle beside it is adjacent, not vertical.

Worked example

Problem: Two lines cross. One angle is 73°. What is the vertical angle across from it?

Step 1: The angle across from 73° is a vertical angle.

Step 2: Vertical angles are equal.

Answer: The vertical angle is 73°.

Finding the angle beside a vertical angle

Sometimes a problem gives one angle and asks for a nearby angle instead of the opposite angle.

Angles beside each other on a straight line are supplementary, so they add to 180°.

Example: If one angle is 73°, the angle beside it is 180° - 73° = 107°.

Vertical angles with algebra

Vertical angles are often used in equations.

Example: one vertical angle is 4x + 8 and the opposite vertical angle is 68°.

Because vertical angles are equal, write 4x + 8 = 68. Then 4x = 60, so x = 15.

Common mistakes

Do not call side-by-side angles vertical angles. Vertical angles are opposite, not adjacent.

Do not add vertical angles to find 180°. Vertical angles are equal to each other.

Use the crossing point as your guide. If the angles face each other across that point, they are vertical angles.

Quick practice

1. If one vertical angle is 41°, the opposite vertical angle is 41°.

2. If one angle is 120°, the angle beside it on a straight line is 60°.

3. If two opposite angles are labeled x and 88°, then x = 88°.

4. If an angle beside 35° is missing, the missing angle is 145° because 180° - 35° = 145°.