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 (90^{o}), then they are complementary

If two adjacent angles form a straight angle (180^{o}), then they are supplementary.

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.

Video Examples: Adjacent Angles

Solved Example on Adjacent Angles

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

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 = 32^{o} and m∠DAB = 58^{o}.