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.

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

Angles

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines