Linear Pair

Definition of Linear Pair

Linear Pair is a pair of adjacent angles that form a straight line.

More About Linear Pair

  • The sum of the measure of the angles in a linear pair is supplementary or 180°.
  • If one angle of a linear pair is acute (below 90°), then the other angle is obtuse (above 90°).

Example of Linear Pair

    example of  Linear Pair

    In the above figure, ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, and ∠4 and ∠1 are linear pairs, as any pair of these angles forms a straight line.

Video Examples: Linear Pairs and Vertical Angles


Solved Example on Linear Pair

Ques: If m∠CAB = 32, then find the m∠CAD in the figure shown.

    example of  Linear Pair
    Choices:
    A. 148
    B. 212
    C. 158
    D. 32
    Correct Answer: A

Solution:

    Step 1: If ∠DAB is a straight angle, then m∠CAD + m∠CAB = 180 [Angle Addition Postulate.]
    Step 2: m∠CAD + 32° = 180° [Substitute.]
    Step 3: m∠CAD = 148 [Simplify.]

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