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# Alternate Exterior and Linear Pair of Angles

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0 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.