How to Find Vertical Angles? (+FREE Worksheet!)

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.

Find the number of degrees.

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

\(3x+50=5x+10→3x+50-50=5x+10-50→3x=5x-40→3x-5x=-40→-2x=-40→x=20\)

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

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

Find the number of degrees.

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

\(4x=6x-22→4x-6x=-22→-2x=-22→x=11\)

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

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