How to Find Vertical Angles

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. \(x=30\)

Related to "How to Find Vertical Angles"

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