If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Geometry (all content)>Unit 2

Lesson 6: Vertical, complementary, and supplementary angles

# Vertical angles review

Review the basics of vertical angles, and try some practice problems.

## Vertical angles

Vertical angles are angles opposite each other where two lines cross.
For example, $\mathrm{\angle }AXD$ and $\mathrm{\angle }BXC$ are vertical angles in the following diagram:

### Practice set

Problem 1A
Are $\mathrm{\angle }APD$ and $\mathrm{\angle }CPB$ vertical angles?
All segments that appear straight are straight.

Want to try more problems like this? Check out this exercise.

## Use vertical angles to find a missing angle measure

Let's look at an example.
What is the measure of angle $x$?
First, let's find the measure of the pink angle:
The pink and blue angles add up to ${180}^{\circ }$ because they are adjacent and form a straight line.
$\text{pink angle}={180}^{\circ }-{121}^{\circ }={59}^{\circ }$
The pink and green angles also add up to ${180}^{\circ }$ because they are adjacent and form a straight line too.
$\text{green angle}={180}^{\circ }-{59}^{\circ }={121}^{\circ }$
The measure of angle $x={121}^{\circ }$.

### Practice

Problem 2A
What is the measure of angle $x$?
${}^{\circ }$

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• I'm not sure if you could see what i could see. but for the practice set like the last one #3... how is angle DYE not vertical with AZB?
• Because they do not share the same vertex
• Are vertical angles always equal? Because in some practices they weren't, and I didn't get why.
• Yes, vertical angles are always equal. Adjacent angles are not always equal though.
• If I eat a pie then eat another pie how old is King charles
• Which one? King Charles the first, second, or third? King Charles the third is seventy-four years (at the time I am writing this), the second was fifty-four when he died, and the first was forty-eight when he passed away. I would need to know when you ate the pies or at what date you would like to know the age of the former and/or present kings. Eating two pies consecutively after another changes everything though that leaves the time from around 5th Century BC to present time or beyond.
• When ever I try to do this Use vertical angles to find a missing angle measure, it always becomes the same answer to the angle I already know. How do you do this question?
• Indeed, verticle angles are always the same measure. The reason they wanted you to do the equation was so that you simply noticed this pattern and learned why this pattern always applies to vertical angles.
• how do you get the answer