Vertical Angles (video Lessons, Examples And Solutions)

Vertical Angles

In geometry, pairs of angles can relate to each other in several ways. When two lines intersect, they form four angles. The opposite angles form vertical angles or vertically opposite angles. They are called vertical angles because they share the same vertex.

The Vertical Angle Theorem states that Vertical angles are equal.

The following diagram shows the vertical angles formed from two intersecting lines. Scroll down the page for more examples and solutions.

Notice also that x and y are supplementary angles i.e. their sum is 180°.

Geometry Worksheets Practice your skills with the following geometry worksheets: Printable & Online Geometry Worksheets

The following diagram shows another example of vertical angles.

The following video explains more about vertical angles.

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How to define and identify vertical angles?

A group of examples that identifies vertical angles.

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Solving Problems using Vertical Angles

Very often math questions will require you to work out the values of angles given in diagrams by applying the relationships between the pairs of angles.

Example: Given the diagram below, determine the values of the angles x, y and z.

Solution: Step 1: x is a supplement of 65°. Therefore, x + 65° = 180° ⇒ x = 180° – 65° = 115°

Step 2: z and 115° are vertical angles. Therefore, z = 115°

Step 3: y and 65° are vertical angles. Therefore, y = 65°

Answer: x = 115°, y = 65° and z = 115°

Example: Both AEC and DEB are straight lines.  Find q.

 

Solution: ∠AEB = ∠DEC    ← vertical angles  q + 45˚= 135˚    q = 135˚ – 45˚ = 90˚

The following video shows how to find a missing vertical angle in a triangle.

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Proof of the Vertical Angle Theorem

The following videos will prove that vertical angles are equal.

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