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Vertical Angles

What are Vetical Angles?

Vertical angles are the angles that are opposite each other when two straight lines intersect. (Technically, these two lines need to be on the same plane)

Vertical angles are congruent(in other words they have the same angle measuremnt or size as the diagram below shows.)

Diagram 1
vertical angles

m$$ \angle x $$ in digram 1 is $$ 157^{\circ}$$ since its vertical angle is $$ 157^{\circ}$$.

Picture 1

picture of vertical example and a non example

Picture 2

Vertical Angles

In Picture 2, $$ \angle $$ 1 and $$ \angle $$2 are vertical angles. Likewise, $$ \angle $$A and $$ \angle $$ B are vertical. Vertical angles are always congruent (have the same measure).

Picture 3

picture of color coded vertical angles

Picture 3 is another picture of vertical angles. The blue pair and red pair of angles are congruent pairs of vertical angles.

Interactive Vertical Angles

Click and the points below to see the rule for vertical angles in action.

A 90
B 90
Drag Points Of The Lines To Start Demonstration

Full Size Interactive Vertical Angles

Practice Problems

Use the theorem that vertical angles are congruent to find the value of x in the problems below.

Problem 1

What is the m $$ \angle $$ B ?

Vertical Angles Picture

Angle B is $$ 130° $$

Example 2
Vertical Angles Algebra

Vertical Angle problems can also involve algebraic expressions. To find the value of x, set the measure of the 2 vertical angles equal, then solve the equation: $ x + 4 = 2x-3 \\ x= 8 $

Problem 2

What is the value of x?

Vertical Angles Example

$ x -2 = 133 \\ x = 133 + 2 \\ x = \boxed{ 135} $

Problem 3

What is the value of x?

Vertical Angles Diagram

$ 2x + 5 = 105 \\ 2x = 100 \\ \frac 1 2 (2x) = \frac 1 2 (100) \\ x = \boxed{ 50} $

Problem 4

Use the vertical angles theorem to solve for x

Vertical Angles Theorem

$ 4x + 7 = 131 \\ 4x = 124 \\ \frac 1 4 (4x) = \frac 1 4 (124) \\ x = \boxed{ 31} $

Problem 5

Find the value of x?

Solving Vertical Angles Problem
Vertical Angles Theorem
Problem 6

Use your knowledge of vertical angles to solve for x

Vertical Angles Problem
vertical angles equation
Problem 7

Solve for x

Vertical Angle Practice Problem
vertical angles equation
Problem 8

Use vertical angles to find the value of x

Problem 6
vertical angles equation
Problem 9

Use vertical angles to find the value of x

Problem 7
vertical angles equation
Problem 10

Use vertical angles to solve for x

Problem 8
vertical angles equation