Understanding the Linear Pair Theorem: Explained with Examples

Linear Pair Theorem

The Linear Pair Theorem states that if two angles form a linear pair, then their measures add up to 180 degrees

The Linear Pair Theorem states that if two angles form a linear pair, then their measures add up to 180 degrees.

To understand this theorem, let’s first define what a linear pair is. A linear pair consists of two adjacent angles that share a common side and their non-common sides form a straight line. In other words, the angles are side by side, and their sum is equal to a straight angle, which measures 180 degrees.

For example, consider angle ABC and angle CBD, where angle ABC and angle CBD share the side BC. If angle ABC measures x degrees and angle CBD measures y degrees, then according to the Linear Pair Theorem, their measures add up to 180 degrees:

x + y = 180

This equation holds true for any linear pair of angles. It can be used to solve problems involving linear pairs, such as finding the measures of individual angles given the sum of their measures or finding the missing angle in a linear pair.

For instance, let’s say we have a linear pair formed by angle ABD and angle DBE, as shown:

A
\
\_____B
/ /
D /
\ /
\ /
E

If we are given that angle ABD measures 80 degrees, we can use the Linear Pair Theorem to find the measure of angle DBE. Since the sum of the measures of a linear pair is 180 degrees, we can set up the equation:

80 + DBE = 180

To solve for DBE, we subtract 80 from both sides:

DBE = 180 – 80
DBE = 100

Therefore, angle DBE measures 100 degrees.

In summary, the Linear Pair Theorem states that two angles forming a linear pair will have measures that add up to 180 degrees. This theorem is used to solve problems involving linear pairs and find missing angle measures.

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