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
If two adjacent angles form a straight angle (180o), 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.
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.
Step 1: Lets first draw the figure.
⇒ m∠DAB = m∠BAC + m∠CAD
⇒ m∠CAD = m∠DAB ∠ m∠BAC
Step 3: = 58o - 32o = 26o
Step 4: So, m∠CAD = 26o