adjacent angles


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.

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.

More about Adjacent Angles

  • If two adjacent angles form a right angle (90°), then they are complementary.




  • If two adjacent angles form a straight angle (180°), then they are supplementary.

Solved Example on Adjacent Angles

Example 1



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.

Ða and Ðb,   Ðb and Ðc,   Ðc and Ðd,   Ðd and Ðe,   Ðe and Ða are the pairs of adjacent angels in the diagram shown above.

 

Example 2



ÐBAC and ÐCAD are adjacent angles. Find mÐCAD, if mÐBAC = 32° and mÐDAB = 58°.


Solution:

 

Step 1: Let’s first draw the figure.

 



Step 2: ÐBAC and ÐCAD are adjacent angles.

 

                        mÐDAB = mÐBAC + mÐCAD

 

            Þ        mÐCAD = mÐDABmÐBAC

 


Step 3:        = 58°32° = 26°

 

Step 4:     So, mÐCAD = 26°.

 

Related Terms for Adjacent Angles

  • Vertex
  • Side
  • Angle