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)

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

##### Example 1

m$$ \angle x $$ in the diagram on the left is $$ 157^{\circ}$$ since its vertical angle is $$ 157^{\circ}$$ .

**Practice** Problems

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

Angle B is 130°

##### Example 2

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

x-2 =133 x = 135°

2x+5 = 105°

2x = 100
$$ \frac{1}{2} (2x=100)
\\
x = 50
$$

4x +7 = 131°

4x = 124

¼(4x = 124) x = 31