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Each pair form supplementary angles because their sum is 180^o. There might be two angles that sum up to 180^o, but that do not form a linear pair. For example, two angles in a parallelogram that share a common side.
One supplementary angle equals the difference between 180° and the other supplementary angle. The adjacent angles formed by two intersecting lines are always supplementary. Angles in a linear pair are always supplementary, but two supplementary angles need not form a linear pair.
Linear Pair of Angles vs. Supplementary Angles. It is the most common mistake to confuse supplementary angles with linear pairs of angles due to similarity in their properties. However, these are two different terms. Let’s understand the difference.
If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°. Hence, a linear pair of angles always add up to 180°.
A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary (add up to \(180^{\circ}\)). \(\angle PSQ\) and \(\angle QSR\) are a linear pair.
A linear pair of angles comprises a pair of angles formed by the intersection of two straight. Thus, two angles are said to form a linear pair if they are adjacent (next to each other) and supplementary (measures add up to 180°.) In the below figure, ∠ABC and ∠CBD form a linear pair of angles.
Linear Pair vs. Supplementary Angles. If two angles add up to 180°, we call them supplementary angles. At first, this naming seems redundant because linear pairs add up the same value. However, there is a subtle difference between the two: Supplementary angles do not necessarily have to be adjacent to one another.
Learn Practice Download. Supplementary Angles. Supplementary angles refer to the pair of angles that always sum up to 180°. The word 'supplementary' means 'something when supplied to complete a thing'. Therefore, these two angles are called supplements of each other.
When two angles form a linear pair, it means that they are adjacent angles, sharing a common side, and their non-common sides form a straight line. In other words, the two angles are adjacent and add up to 180 degrees. Such angles are always supplementary.
Since the non-adjacent sides of a linear pair form a line, a linear pair of angles is always supplementary. However, just because two angles are supplementary does not mean they form a linear pair. In the diagram below, ∠ABC and ∠DBE are supplementary since 30°+150°=180°, but they do not form a linear pair since they are not adjacent.