# How to Find Vertical Angles

In this article, you will learn how to Find Vertical angles in a few simple steps.

## Step by step guide to Finding Vertical angles

The intersecting lines form an $$X$$-shape, and the angles on the two opposite sides of this $$X$$ are called vertical angles. The two vertical angles are always the same size and they have the same vertex. The bisector of two vertical angles makes a straight angle.

In the diagram at the right, lines  and are straight:

• Angle$$1$$+ Angle$$3$$=$$180$$(because it is a straight angle)
• Angle$$2$$+ Angle$$3$$=$$180$$(because it is a straight angle)

Infer from the above two relations that angle $$1$$ and $$2$$ angle are equal; So, the vertical angles are equal.

In this diagram:

• Angle $$1$$ and angle $$2$$ are vertical angles.
• Angle $$3$$ and angle $$4$$ are vertical angles.
• Angle $$1$$ and angle $$3$$ are NOT vertical angles.

### Finding Vertical Angles Example 1:

Find the number of degrees.

Solution: $$(3x+50)^{\circ}$$ and $$(5x+10)^{\circ}$$ are vertical angles.

$$3x+50=5x+10→3x+50-50=5x+10-50→3x=5x-40→3x-5x=-40→-2x=-40→x=20$$

$$(3x+50)^{\circ}=(3(20)+50)=110^{\circ}$$

$$(5x+10)^{\circ}=(5(20)+10=110^{\circ}$$

### Finding Vertical Angles Example 2:

Find the number of degrees.

Solution: $$(4x)^{\circ}$$ and $$(6x-22)^{\circ}$$ are vertical angles.

$$4x=6x-22→4x-6x=-22→-2x=-22→x=11$$

$$(4x)^{\circ}=(4(11))=44^{\circ}$$

$$(6x-22)^{\circ}=(6(11)-22=44^{\circ}$$

## Exercises for Finding Vertical Angles

### Find the value of $$x$$.

1)

2)

1. $$x=96$$
2. $$x=30$$

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