CTET Paper II (Mathematics and Science) 21 Dec 2021 Solved Paper

Concept:A linear pair consists of two adjacent angles whose non‑common sides form a straight line, and their sum is $180^\circ$. Adjacent angles share a common vertex and a common side, but do not overlap.Explanation:Since $O$ lies on line $AB$, the rays $OA$ and $OB$ are opposite. Ray $OC$ is drawn from $O$ to a point $C$ not on $AB$.For statement (a): $\angle AOC$ and $\angle BOC$ are adjacent (they share vertex $O$ and side $OC$) and their non‑common sides $OA$ and $OB$ form a straight line. Therefore, $\angle AOC + \angle BOC = 180^\circ$, so they form a linear pair. This is true.For statement (b): $\angle AOB$ is a straight angle ($180^\circ$) with arms $OA$ and $OB$. $\angle BOC$ has arms $OB$ and $OC$. Although they share vertex $O$ and side $OB$, they overlap in interior – the region of $\angle AOB$ (the half‑plane) contains the interior of $\angle BOC$. Hence they are not adjacent angles. This is false.Answer:Only (a) is true. Option A.