Home
Arithmetic
Algebra
Geometry
Statistics
Probability
Set Theory
Trigonometry
Matrices
SAT Preparation
ACT Preparation
GMAT Preparation
Math Worksheets
Math Games
Math Trivia
Chemistry
How Things Work
Animal Facts
Links

Alternate Interior Angles & Alternate External Angles

In geometry, pairs of angles can relate to each other in several ways. In this lesson, we will be describing alternate interior angles and alternate exterior amgles.

 

 

Alternate Interior Angles

When a line intersects a pair of parallel lines alternate interior angles are formed. Alternate interior angles are equal to each other.

alt interior angles  alt interior angles

One way to find the alternate interior angles is to draw a zigzag line on the diagram. In the above diagrams, d and e are alternate interior angles. Similarly, c and f are also alternate interior angles.

 

 

Example 1: Given the diagram below, determine the values of the angles b, c, d, e, f, g and h.

alt interior angles

Solution:

Step 1: b is a supplement of 60°.

            Therefore, b + 60° =180° ⇒ b = 180° – 60° = 120°

Step 2: b and c are vertical angles.

            Therefore, c = b = 120°

Step 3: d and 60° are vertical angles.

            Therefore, d = 60°

Step 4: d and e are alternate interior angles.

            Therefore, e = d = 60°

Step 5: f and e are supplementary angles.

            Therefore, f + 60° =180° ⇒ f = 180° – 60° = 120°

Step 6: g and f are vertical angles.

            Therefore, g = f = 120°

Step 7: h and e are vertical angles.

            Therefore, h = e = 60°

Answer: b = 120°, c = 120°, d = 60°, e = 60°, f = 120°, g = 120° and h = 60°

From the above example, you may notice that either an angle is 60° or it is 120°. Actually, all the small angles are 60° and all the big angles are 120°. In general, the diagram will be as shown below. The small and big pair of angles are supplementary (i.e. small + big = 180°). Therefore, given any one angle you would be able to work out the values of all the other angles.

alt interior angles - big & small

 

 

Alternate Exterior Angles

One way to remember alternate exterior angles is that they are the vertical angles of the alternate interior angles. Alternate exterior angles are equal to one another.

alt exterior angles

a and h are alternate exterior angles and they are equal to one another.

b and g are alternate exterior angles and they are equal to one another.

 

 

Custom Search

 


Useful Links:
Math.com - Pairs of Angles
Sparknotes - Pairs of Angles
 

© Copyright 2005, 2007 - onlinemathlearning.com

 

Custom Search