Alternate Exterior and Linear Pair of Angles

Alternate exterior angles are studied in the discipline of mathematical building. Alternate external angles are all those angles that are generally created when 2 or more lines cross with another transversal line.

A transversal line is defined as any line which crosses 2 straight lines at a certain place. Therefore, the alternative outside angles is the angles created on most of the exterior sides of the crossing transversal line. Well with the following example, we will have a better knowledge of the topic. There are 2 straight segments in the illustration above – k & l. Because ‘T’ denotes the transversal line, 2 sets of alternative exterior angles are generated on the external sides of the transversal lines. ‘T’ can be A and B, C and D.

In this article, we are going to discuss what alternate exterior angles are and what linear pairs of angles mean.

What is the Linear Pair of Angles?

A linear pair of angles is defined as a pair of neighbouring angles generated when 2 distinct lines contact one other at a junction when developing geometry. Adjacent angles are generated when 2 angles share a similar vertex as well as a common arm while they do not overlap one another. Angles in linear pairs always are supplementary to each other because they form a straight line. Simply said, the sum of these two angles in a linear pair always equals 180 degrees.

Whenever two lines intersect at a point, we can see a linear pair, so how do we understand it?

The sum of angles 1 and 2 is 180-degrees.

For instance, consider 2 intersecting lines that converge at a central point. The produced linear pair of angles can be next to each other as follows:

∠F and ∠G

∠G and ∠H

∠H and ∠I

∠F and ∠I

Let’s go through a solved example to understand the concept in an easy & fun manner.

Solved Example for Alternate Exterior and Linear Pair of Angles

We have been given information on alternate exterior angles, the value of given angle ‘a’ = 3x – 33 degrees, and angle ‘h’ = 2x +26 degrees. We also notice one thing Lines L1 and L2 are parallel, so we can say that the angles ‘a’ and ‘h’ are congruent.

Now, we know that angle a  = angle h (Since the angles are congruent)

So, 3x – 33 equals 2x + 26

Let’s solve the equation by putting the variables on one side and the numbers on the other side.

3x- 2x = 26+33 , x = 59

Here, the value of ‘x’ comes out as 59-degrees.

So, substituting the values in the given equations we get the values of the angle a = 3 * 59 – 33 = 84 degrees, and Angle h = 2x + 26 = 2 * 59 + 26 = 144 degrees

Now, to find out linear pairs, we have the following method:

Here, we know that a + b = 180, so 84 + b = 180

We get  the value of angle b = 96 degrees

So, the first linear pair we get is (84, 96).

Similarly, angle ‘h’ = 144, so angle g = 180 – h, i.e.,180 – 144 equals to 36 degrees

So, another linear pair, we get here is (36, 144).

Theorems Concerning Alternate Exterior Angles

The following is stated in the alternative exterior theorem: If a traversal intersects 2 parallel lines, then the alternate exterior angles created are referred to as ‘congruent angles,’ which are also known as angles that have the same measurement. 

Do you want to learn more about these fascinating topics? Then go to Cuemath’s Website & learn more about these angles as well as other angles-related theorems.