If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Algebra basics

Unit 8: lesson 1.

Equation practice with vertical angles

Study.com

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.

Vertical Angles

Vertical Angles are the angles opposite each other when two lines cross

Example: a° and b° are vertical angles.

The interesting thing here is that vertical angles are equal :

(in fact they are congruent angles )

Have a play with them yourself. Notice how the 4 angles are actually two pairs of "vertical angles":

Example: Find angles a°, b° and c° below:

Because b° is vertically opposite 40°, it must also be 40°

A full circle is 360°, so that leaves 360° − 2×40° = 280°

Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each.

Answer: a = 140° , b = 40° and c = 140° .

Vertical Angles

In these lessons, we will learn

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.

vertical angles

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.

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.

Proof of the Vertical Angle Theorem

The following videos will prove that vertical angles are equal.

Mathway Calculator Widget

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

Vertical angles are congruent diagram.

IMAGES

  1. Question Video: Solving Problems Involving Adjacent Angles

    how to solve vertical angles questions

  2. How To Solve Vertical Angles With One Variable

    how to solve vertical angles questions

  3. How To Solve Vertical Angles

    how to solve vertical angles questions

  4. How To Solve Vertical Angles With One Variable

    how to solve vertical angles questions

  5. please help! Remember what we know about vertical angles and solve for x. Answer:

    how to solve vertical angles questions

  6. How To Solve Vertical Angles

    how to solve vertical angles questions

VIDEO

  1. Vertically opposite angles are equal

  2. Vertical Angles & Proofs

  3. Corresponding and Vertical Angles

  4. how to solve Rubik cube

  5. Frequently Asked Questions From Lines and Angles

  6. TCL 55" LED TV Vertical Bar Problem Easy Solution #Sk Soni Group #How To Solve Vertical Bar LED TV

COMMENTS

  1. What Are Examples of Vertical Angles in Real Life?

    The intersecting lines on the dartboard form 10 pairs of vertical angles. The angles lie opposite of each other on the board and share the same measurement. The bull’s eye in the center of the board serves as the vertex.

  2. What Is an Opposite Angle?

    Opposite angles, known as vertically opposite angles, are angles that are opposite to each other when two lines intersect. Vertically opposite angles are congruent, meaning they are equal in degrees of measurement.

  3. What Is a Reference Angle?

    A reference angle is an angle formed by the x-axis and the terminal side of a given angle, excluding quadrantal angles. It is a helpful tool when finding the values of trigonometric functions belonging to particular angles.

  4. Equation practice with vertical angles (video)

    If the angles are vertical, then they are congruent, or the same measure. Therefore, if a vertical equals 3x and the other equals 80-x, you would simply set up

  5. Equation practice with vertical angles

    Equation practice with vertical angles. CCSS.Math: 8.EE.C.7, 8.EE.C.7b. Problem. Solve for x x xx: Created with Raphaël 7 x + 15 6 ∘ 7x + 156^\circ

  6. Solving Equations

    Watch and learn how to find the measure of vertical angles by setting expressions equal to each other.

  7. Vertical Angles

    Vertical angles are congruent, so set the angles equal to each other and solve for x . Then go back to find the measure of each angle.

  8. How to Solve Equations Involving Vertical Angles

    Step 1: Set the expressions labeling the angles equal to each other. Step 2: Isolate the variable on one side of

  9. Solving Equations Involving Vertical Angles Practice

    Solving Equations Involving Vertical Angles · 1. Find the value of x x by analyzing the relationship of vertical angles below. · 2. Which corresponds to the value

  10. Vertical Angles

    Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each. Answer: a = 140°, b = 40° and c = 140°. Note: They are also called

  11. Vertical Angles (video lessons, examples and solutions)

    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

  12. 2.4 Vertical Angles

    b. a3 and a4 are neither vertical angles nor a linear pair. ... Practice and Applications.

  13. Vertical angles

    and they form a straight line when they are next to one another. You can solve for missing supplementary angles to see why

  14. Page 2 of 3

    Vertical angles practice problem. Find missing angles given one angle. First, identify the two sets of vertical angles. Angles