Question

In the given figure identify:
(i) Five pairs of adjacent angles.
(ii) Three linear pairs.
(iii) Two pairs of vertically opposite angles.

Answer 1

Part (i),
Angles that share a common arm, common vertex and the non common arms lie on the either side of the common arm are called adjacent angles.
$(\angle AOE,\angle EOC)$, $(\angle EOC,\angle COB)$, $(\angle COB,\angle BOD)$, $(\angle BOD,\angle AOD)$ and $(\angle AOC,\angle BOC)$ are five pairs of adjacent angles.

Part (ii),
The adjacent angles whose non common arms form a straight line are called linear pairs of angles.
$(\angle AOE,\angle BOE)$, $(\angle AOC,\angle BOC)$ and $(\angle BOC,\angle BOD)$ are linear pair of angles.

Part (iii),
The non-adjacent angles formed by the intersection of two lines are called vertically opposite angles.
Here two lines AB and CD intersect at point O.
$(\angle AOD,\angle COB)$ and $(\angle AOC,\angle BOD)$ are vertically opposite angles.