Which one of the pairs of angles below is adjacent


Question: Which one of the pairs of angles below is adjacent?

Pairs of angles

Any two angles that share a common ray or side, a common vertex, and whose interiors do not overlap are called adjacent angles.

Answer: (a)

We will use the definition of adjacent angles to determine the pairs of adjacent angles.

Explanation:

(a) Clearly, ∠1 and ∠2 have a common vertex O and a common arm OB. They have non-common arms OA  and OC on both sides of the common arm OB. So, ∠1 and ∠2 are adjacent angles.

(b) Clearly, ∠1 and ∠2 have a common arm as OB. But ∠1 have a vertex as X and ∠2 have a vertex as O. They don't have a common vertex. So, ∠1 and ∠2 are not adjacent angles.