# Vertical 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)

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

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