Which one of the pairs of angles below is adjacent?
Any two angles that share a common ray or side, a common vertex, and whose interiors do not overlap are called adjacent angles.
Answer: Angles shown in option (a) are adjacent angles, as they share a common vertex, a common arm, and do not overlap.
We will use the definition of adjacent angles to determine the pair of adjacent angles.
(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 has a vertex as X and ∠2 has a vertex as O. So, they don't have a common vertex. So, ∠1 and ∠2 are not adjacent angles.