What is the difference between a linear pair and a pair of …

Supplementary Angles

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Linear Algebra

Trigonometry (mathematics)

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What is the difference between a linear pair and a pair of supplementary angles?

2 Answers

Robert Nichols

Robert Nichols

Linear Pairs are a special subset of supplementary angles.

SupplementaryAngles are any two angles that sum to 180 degrees.

Linear pairs are any two angles that share a common ray and sum to 180 degrees.

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Chetan Sharma

Chetan Sharma , studied at Post Graduation in Mathematics

There is a difference.

Linear pair requires angles to adjacent i.e Two angles must have one common arm.

But

In case of supplementary angles, angles need not to be adjacent.

Linear pair angles are always supplementary.

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Home > Math > Geometry > Topics > Supplementary Angles

Supplementary Angles

The definition of supplementary is two angles whose sum is 180° are supplementary. The angles can be either adjacent (share a common side and a common vertex and are side-by-side) or non-adjacent.

Example 1. Given m 1 = 45° and m 2=135° determine if the two angles are supplementary.

45° + 135° = 180° therefore the angles are supplementary.

We will use the following facts to help us determine if two angles are supplementary.

  • A linear pair is two angles that are adjacent and form a line.

  • The angle measure of a line is 180°
  • If two angles form a linear pair then they are supplementary.

Example 2: the angles form a line (linear pair) therefore they are supplementary

Example 3: the angles can be non-adjacent as long as their sum is 180°

110°+ 70° = 180° The sum is 180° therefore they are supplementary.

Example 4:

1 and 2 form a linear pair so m 1 + m 2 = 180° therefore the angles are supplementary.

How many other linear pairs can you see in the diagram?

m 2 + m 3 = 180°
   
m 3 + m 4 = 180°
   
m 1 + m 4 = 180°

Remember that linear pairs are supplementary and that 2 intersecting lines will form 4 pairs of supplementary angles.

Geometry & Algebra: find the value of x the find the m ABD and m DBC.

Write an equation

(4x +6) ° + (11x – 6)°= 180°

Identify like terms

(4x +6) ° + (11x6)°= 180°

Combine like terms

4x + 11x +66 = 180°

15x + 0 = 180°

The zero is unnecessary  =
Divide both sides by 15

x = 12


m ABD = 4x + 6 = 4(12)+6 = 54°

m DBC = 11x – 6 = 11(12) -6 = 126°

check your answer

54° + 126° = 180°

Sum it up: Supplementary angles are two angles whose sum is 180°. A linear pair (two angles that form a line) will always be supplementary. The two angles can be adjacent or non-adjacent.

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Complementary Angles

Complementary or Supplementary

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