Question

Name the four pairs of supplementary angles shown in figure.

Answer 1

Hint:Two Angles are Supplementary when they add up to 180 degree or form a linear pair. Observe the diagram and name the four pairs of supplementary angles in which they form a linear pair or sum of two angles 180 degree.

Complete step-by-step answer:
The two adjacent angles which share a common point with opposite rays forms a linear pair of angles. These angles add up to a straight angle, which makes a supplementary angle.
A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.
According to the given figure,

Here $\angle $AOC and $\angle $AOD form a linear pair in which they meet at a common point at O and when we add up these two angles we get 180 degree i.e Supplementary angles.
Similarly by observing the diagram we can write other pairs of supplementary angles as follows
$\angle $AOC and $\angle $COB
$\angle $AOD and $\angle $DOB
$\angle $DOB and $\angle $BOC
These are the names of four pairs of supplementary angles.

Note: Students should know the definitions of supplementary and complementary angles i.e If the sum of two angles is 180 degree then they are said to be supplementary angles,which forms linear pair.Whereas If the sum of two angles is 90 degree then they are said to be Complementary angles,which forms right angle.In above question $\angle $AOC and $\angle $DOB cannot form supplementary angles although they meet at common point but they are not adjacent angles ,they are vertically opposite angles.