Adjacent Angles



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:

adjacent angles image, 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.

problems on adjacent angles, adjacent angles


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
  • Basic Geometrical Concepts
  • Angles
  • Classification of Angles
  • Related Angles
  • Some Geometric Terms and Results
  • Complementary Angles
  • Supplementary Angles
  • Complementary and Supplementary Angles
  • Adjacent Angles
  • Linear Pair of Angles
  • Vertically Opposite Angles
  • Parallel Lines
  • Transversal Line
  • Parallel and Transversal Lines

  • 7th Grade Math Problems

    8th Grade Math Practice

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