You are watching: If two angles form a linear pair, then they are supplementary angles.
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.
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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) ° + (11x - 6)°= 180°Combine like terms4x + 11x +6 - 6 = 180°15x + 0 = 180°The zero is unnecessary
Divide both sides by 15x = 12m ABD = 4x + 6 = 4(12)+6 = 54°m DBC = 11x - 6 = 11(12) -6 = 126°check your answer54° + 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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