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 (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.

Solution:

Step 1: Lets first draw the figure.

Step 2: ∠BAC and ∠CAD are adjacent angles.
⇒ m∠DAB = m∠BAC + m∠CAD
⇒ m∠CAD = m∠DAB ∠ m∠BAC
Step 3: = 58^o - 32^o = 26^o
Step 4: So, m∠CAD = 26^o

 

Related Worksheet

• Parallel-Lines-and-Transversals-Gr-8