**Two angles are said to be adjacent angles, if; **

(i) they have a common vertex,

(ii) they have a common arm and

(iii) the other arms of the two angles lie on opposite sides of the common arm.

**The given figure below shows a pair of adjacent angles:**

(i) they have a common vertex (O).

(ii) they have a common arm (OB) and (iii) the other arms OA and OC of the two angles are on opposite sides of the common arm OB.

**Explanation:**

∠AOB and ∠BOC have the common vertex O. Also they have a common arm OB and their other arms OA and OC lie on the opposite sides of the common arm OB. Therefore, ∠AOB and ∠BOC are adjacent angles.

∠AOC and ∠AOB are not adjacent angles, because their other arms OC and OB are not on the opposite sides of the common arm OA.

Worked-out problems on adjacent angles:

Are the following angles adjacent? Give reasons.

**Solution:**

(a) ∠1 and ∠2 are not adjacent because they do not have a common arm.

(b) ∠1 and ∠2 are not adjacent because their interiors overlap.

(c) ∠1 and ∠2 are not adjacent because they do not have a common vertex.

(d) ∠1 and ∠2 are adjacent because they have a common arm, a common vertex and interiors do not overlap.

●** Lines and Angles**

**Fundamental Geometrical Concepts**

**Some Geometric Terms and Results**

**Complementary and Supplementary Angles**

**Parallel and Transversal Lines**

**8th Grade Math Practice**** ****From Adjacent Angles to HOME PAGE**

**Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.