Adjacent Angles

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Definition of Adjacent Angles

The word "adjacent" means "next" or "neighboring"

Adjacent angles are angles just next to each other. Adjacent angles share a common vertex and a common side, but do not overlap.

More about Adjacent Angles

    If two adjacent angles form a right angle (90o), then they are complementary
    example of Adjacent Angles
    If two adjacent angles form a straight angle (180o), then they are supplementary.
    example of Adjacent Angles

Examples of Adjacent Angles

    In the figure shown, a and b are adjacent angles. They have a common vertex O and a common side OA.
    example of Adjacent Angles

Video Examples: Adjacent Angles


Solved Example on Adjacent Angles

Name all pairs of angles in the diagram that are adjacent.

    example of Adjacent Angles

Solution:

    Adjacent angles are angles just next to each other. Adjacent angles share a common vertex and a common side, but do not overlap.
    ∠a and ∠b,
    ∠b and ∠c
    ∠c and ∠d
    ∠d and ∠e
    ∠e and ∠a are the pairs of adjacent angels in the diagram shown above.

∠BAC and ∠CAD are adjacent angles. Find m∠CAD, if m∠BAC = 32o and m∠DAB = 58o.

Solution:

    Step 1: Lets first draw the figure.
      example of Adjacent Angles
    Step 2: ∠BAC and ∠CAD are adjacent angles.
    ⇒ m∠DAB = m∠BAC + m∠CAD
    ⇒ m∠CAD = m∠DAB ∠ m∠BAC
    Step 3: = 58o - 32o = 26o
    Step 4: So, m∠CAD = 26o

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