# Vertical Angles

#### What are Vetical Angles?

Vertical angles are the angles that are opposite each other when two straight lines intersect. (Technically, these two lines need to be on the same plane)

Vertical angles are congruent(in other words they have the same angle measuremnt or size as the diagram below shows.)

Diagram 1

m$$\angle x$$ in digram 1 is $$157^{\circ}$$ since its vertical angle is $$157^{\circ}$$.

Picture 1

Picture 2

In Picture 2, $$\angle$$ 1 and $$\angle$$2 are vertical angles. Likewise, $$\angle$$A and $$\angle$$ B are vertical. Vertical angles are always congruent (have the same measure).

Picture 3

Picture 3 is another picture of vertical angles. The blue pair and red pair of angles are congruent pairs of vertical angles.

### Interactive Vertical Angles

Click and the points below to see the rule for vertical angles in action.

 ∠ A 90 90
Drag Points Of The Lines To Start Demonstration

### Practice Problems

Use the theorem that vertical angles are congruent to find the value of x in the problems below.

##### Problem 1

Angle B is $$130°$$

##### Example 2

Vertical Angle problems can also involve algebraic expressions. To find the value of x, set the measure of the 2 vertical angles equal, then solve the equation: $x + 4 = 2x-3 \\ x= 8$

##### Problem 2

$x -2 = 133 \\ x = 133 + 2 \\ x = \boxed{ 135}$

##### Problem 3

$2x + 5 = 105 \\ 2x = 100 \\ \frac 1 2 (2x) = \frac 1 2 (100) \\ x = \boxed{ 50}$

##### Problem 4

$4x + 7 = 131 \\ 4x = 124 \\ \frac 1 4 (4x) = \frac 1 4 (124) \\ x = \boxed{ 31}$