Page 41 - Ganit Kaushal

Some Special Angles and Their Definitions

If two arms forming an angle lie in a straight line, then such an angle is called
a straight angle. In the adjoining figure, the two arms OA and OB forming A O B
∠AOB lie in a straight line. So, this is an example of a straight angle.

Now, let us observe that any ray OC divides ∠AOB into two angles, namely, ∠AOC and ∠BOC.
C C C

A O B A O O B
Is it possible that angle ∠AOC = ∠BOC?
The answer is yes. Certainly, they can be equal, which gives rise to a special kind of angle known as
a right angle.
If the two angles, ∠AOC and ∠BOC are equal, each of these angles formed is called a right angle. So, we
conclude that a straight angle contains exactly two right angles.

As shown in the figure below, observe that the right angle resembles the shape of the letter ‘L’.
C C C

A O B A O O B
Angles that are smaller than a right angle are called acute angles, and angles that are greater than a right angle
but less than a straight angle are called obtuse angles. Angles that are greater than a straight angle but less than
a full circle or complete angle are called reflex angles.

C C Reflex angle
A D
C O B
Obtuse angle
Acute angle
A
O B A O
If two arms forming an angle overlaps, then the angle is called complete angle. O A B

Two lines are called perpendicular lines if they meet at right angles. m
In the adjacent figure, lines l and m are perpendicular to each other.
l O
The point O, where the lines meet, is known as the point of intersection.

2.4 COMPARING THE ANGLES

The procedure of determining whether one angle is larger or smaller than the other is called ‘comparing the
angles’.
Comparing Angles by Observation

If the difference in rotations between various angles is significant, we can use naked eye observation to determine
which angle is greater and which is smaller.

Lines and Angles 39