# Vertical angles as congruent angles

## Vertical angles are congruent angles

In this lesson we’ll look at how to use vertical angles to solve problems.

Hi! I'm krista.

I create online courses to help you rock your math class. Read more.

**Vertical angles**

Vertical angles are angles in opposite corners of intersecting lines, like these:

So vertical angles always share the same vertex, or corner point of the angle. They’re a special angle pair because their measures are always equal to one another. Therefore, from the diagram we can say

???a{}^\circ =b{}^\circ???

or

???\angle a\cong \angle b???

## How to use vertical (and congruent) angles to solve geometry problems

## Take the course

### Want to learn more about Geoemtry? I have a step-by-step course for that. :)

## Vertical angles that include an unknown value

**Example**

Find the value of ???x???.

???58{}^\circ??? and ???(10x+18){}^\circ??? are vertical angles, and are therefore congruent, so we can set them equal to one another and solve for the variable.

???(10x+18){}^\circ =58{}^\circ???

???10x{}^\circ =40{}^\circ???

???x=4{}^\circ???

Let’s try another one.

Vertical angles are angles in opposite corners of intersecting lines.

**Example**

Solve for the variable.

Use the fact that vertical angles are congruent to complete the triangle on the right. The angle measuring ???(4x+8)^\circ??? has a vertical angle inside the triangle on the right.

The angles in a triangle sum to ???180{}^\circ???, so we can set up an equation to solve for the variable.

???(4x+8){}^\circ +(3x+12){}^\circ +90{}^\circ =180{}^\circ???

???7x{}^\circ +110{}^\circ =180{}^\circ???

???7x{}^\circ =70{}^\circ???

???x=10{}^\circ???