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
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