Up

Exterior Angle Theorem

The Exterior Angle Theorem is not so bad and it’s a very good shortcut to finding the measure of an exterior angle. So, what is an exterior angle?

An exterior angle is when a line is drawn outside of the triangle, extending the angle.

Congruent-Triangles-1

The exterior angle is \(\angle {\text{ACD}}\). All the angles inside the triangle are interior angles.

A little side note: the exterior angle and the adjacent interior angle (the one connected to it) always add up to 180° because together they form a line.

The Exterior Angle Theorem says that an exterior angle of a triangle is equal to the sum of the 2 non-adjacent interior angles.

Taking our above example, \(\angle {\text{ACD}}\) would equal whatever \(\angle {\text{A}}\) + \(\angle {\text{B}}\) equaled because those are the two angles NOT connected to the exterior angle.

Let’s try two fairly basic examples and then try a few tougher ones.

 

Example 1:

Congruent-Triangles-2

What would \(\angle {\text{DFG}}\) measure?

\(\angle {\text{DFG }} = \angle {\text{D }} + \angle {\text{E}}\)

\(\angle {\text{DFG }} = {\text{ 24 }} + {\text{ 34}}\)

\(\angle {\text{DFG }} = {\text{ 58}}^\circ \)

This next example is a backwards one!

Example 2:

Congruent-Triangles-3

Find the measure of x.

\(\angle {\text{JKM }} = \angle {\text{L }} + \angle {\text{M}}\)

\({\text{146 }} = {\text{ 77 }} + {\text{ x}}\)

\( - {\text{77}}     - {\text{77}}\)               
____________________

\({\text{69}}^\circ  = {\text{ x}}\)             

 

Those will be the two basic types of questions that deal with the Exterior Angle Theorem. They can get tougher when they throw in more than one x! But they are all set up the same way.

Example 3:

Congruent-Triangles-4

 

Solve for x.

\(\angle {\text{MED }} = \angle {\text{C }} + \angle {\text{D}}\)

\({\text{11x }}-{\text{ 1}}0{\text{ }} = {\text{ 6x }} + {\text{ 11 }} + {\text{ 39}}\)

\({\text{11x }}-{\text{ 1}}0{\text{ }} = {\text{ 6x }} + {\text{ 5}}0\)                                             (combine like terms)

\({\text{6x}}               - {\text{6x}}\)                                                 (get variable on one side)

________________________

\({\text{5x }}-{\text{ 1}}0{\text{ }} = {\text{ 5}}0\)

\( + {\text{1}}0          +             {\text{1}}0\)
________________________

\({\text{5x}} = {\text{6}}0\)

\({\text{x }} = {\text{ 12}}\)

Example 4:

Congruent-Triangles-5

 

Solve for x.

\(\angle {\text{DEF }} = \angle {\text{G }} + \angle {\text{F}}\)

\({\text{1}}0{\text{x }} + {\text{ 2 }} = {\text{ 2x }} + {\text{ 1 }} + {\text{ 89}}\)

\({\text{1}}0{\text{x }} + {\text{2 }} = {\text{ 2x }} + {\text{ 9}}0\)

\( - {\text{2x}}                  - {\text{2x}}\)
_____________________________

\({\text{8x }} + {\text{ 2 }} = {\text{ 9}}0\)

\( - {\text{2}}                   - {\text{2}}\)

\({\text{8x}} = {\text{88}}\)

\({\text{x }} = {\text{ 11}}\)

Below you can download some free math worksheets and practice.


Downloads:
3631 x

Find the measure of each angle indicated.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Congruent-Triangles-Exterior-Angle-Theorem-Easy

Watch below how to solve this example:

 

Downloads:
2171 x

Solve for x.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Congruent-Triangles-Exterior-Angle-Theorem-Medium

Watch below how to solve this example:

 

Downloads:
1862 x

Find the measure of the angle indicated.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Congruent-Triangles-Exterior-Angle-Theorem-Hard

Watch below how to solve this example:

 
 
 

Facebook PageGoogle PlusTwitterYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems