Page 47 - Ganit Kaushal

2.6 MEASURING THE ANGLES

By now, we have learnt how to compare two angles by means of superimposition and by using transparent
circular sheets.
Can we actually have a method to measure how big an angle is? Can we do it by assigning a number

to an angle without comparing it with another angle?
To measure any quantity, it is very important to know its unit of measurement. For example, we can
say that the distance between two cities is 10 kilometres only when we know the length of one (unit)
kilometre. So, to quantify an angle, it is very important to know the unit of measurement of an angle.

To answer the above questions, mathematicians came up with a great idea. They divided the angle at the centre
of the circle into 360 equal parts (see figure below).
The angle measure of each of these parts is taken as the unit to measure an angle. The angle measure of each
of these unit parts is taken as one degree, which is written as 1°.

120° 110° 100° 90° 80° 70° 60°
130° 50°
140° 40°
150° 30° 10°
160° 20°
10° 5°
170°
0° (360°)
360°
180°
350°
190°
340°
200°
330°
210°
320°
220°
310°
230°
300°
240°
290°
250°
280°
260°
270°
Full circle before division Full circle after division into 360 equal parts
Now, with the help of these unit partitions, each measuring one degree (1°), we
can assign precise measurements to angles.
For example, looking at the adjoining figure, we can say that the measurement
of this angle is 30° as it contains 30 units of 1° each.
It is now easy to understand that the angle
measure of a straight angle is 180°, as it is
half of the full circle,
1
i.e., × 360° = 180°.
2
The angle measure of a right angle is 90°, as
it is one-fourth of the full circle,
1
i.e., × 360° = 90°.
4
These calculations can be easily understood with the help of the
adjoining figures.

Lines and Angles 45