In these lessons, we will learn

- how to identify vertical angles,
- the vertical angle theorem,
- how to solve problems involving vertical angles,
- how to proof vertical angles are equal.

**Related Pages**

Angles

Pairs Of Angles

Types Of Angles

More Geometry Lessons

**Angle Worksheets and Activities**

Find unknown angles worksheet

Find unknown angles using equation worksheet

Find unknown angles word problems worksheet

In geometry, pairs of angles can relate to each other in several ways. When two lines intersect, 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.

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

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

The following diagram shows another example of vertical angles.

The following video explains more about vertical angles.

**How to define and identify vertical angles?**

A group of examples that identifies 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.

The following videos will prove that vertical angles are equal.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.