**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

**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.

**Ð****a** and **Ð****b**,
**Ð****b** and
**Ð****c**,
**Ð****c** and
**Ð****d**,
**Ð****d** and
**Ð****e**,
**Ð****e** and
**Ð****a** are
the pairs of adjacent angels in the diagram shown above.

** **

**Example 2**

**
**

Ð*BAC* and
Ð*CAD *are adjacent
angles. Find *m*Ð*CAD*, if *m*Ð*BAC *= 32° and *m*Ð*DAB*
= 58°.

**Solution:**

**Step 1:**
Let’s first draw the figure.

**Step 2:** Ð*BAC*
and Ð*CAD *are adjacent angles.

*m***Ð***DAB***
= m**

* *

*
***Þ**** m**

**Step 3:**
** =** **
58° – 32°**
= **26°**

** **

**Step 4: **
So,** m**

**Related Terms for Adjacent
Angles**

- Vertex
- Side
- Angle