Supplementary Angles And Complementary Angles

When two line segments or lines meet at a common point, at the point of intersection an angle is formed. When a ray is rotated about its end point, then the measure of its rotation in an anti-clockwise direction is the angle formed between its initial and final position.

Angle

Figure 1

In fig. 1 if the ray \(\small \overrightarrow{OP}\) is rotated in the direction of the ray \(\small \overrightarrow{OQ}\), then the measure of its rotation represents the angle formed by it. In this case, the measure of rotation that is the angle formed between the initial side and the terminal side is represented by Ɵ.

Let us now have a look at complementary angles and supplementary angles.

Complementary Angles

When the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles.

Complementary Angles

Figure 2

In Fig. 2 given above, the measure of angle BOD is 60o and angle AOD measures 30o. On adding both of these angles we get a right angle, therefore ∠BOD and ∠AOD are complementary angles.

The following angles in Fig. 3 given below are complementary to each other as the measure of the sum of both the angles is 90o. ∠POQ and ∠ABC are complementary and are called complements of each other.

Complements

Figure 3

Supplementary Angles

When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up to form a straight angle, then these angles are referred to as supplementary angles.

Supplementary Angles

Figure 4

In Fig. 4 given above, the measure of ∠AOC is 60o and ∠AOB measures 120o. On adding both of these angles we get a straight angle. Therefore, ∠AOC and ∠AOB are supplementary angles, and both of these angles are known as a supplement of each other.

Complementary angles and Supplementary angles differences:

How could remember easily the difference between Complementary angle and supplementary angles?

  • C letter of Complementary stands for “Corner” (A right angle, \(90^{\circ}\) )
  • S letter of Supplementary stands for “Straight” ( a straight line, \(180^{\circ}\)))


Practise This Question

Let f:[0,) [0,2] be defined by f(x)=2x1+x , then f  is