Page 43 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\02_Chapter_2\Chapter_2
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Magnitude of an Angle

Have you ever noticed the angle, by which the door of your room is opened,
when you go outside? If not, look at the picture given here.
P U S H
Think about how much wider you will need to open it to bring a study table
inside the room?

Let us assume that the arm OA of ∠AOB is fixed and arm OB rotates about
the vertex O, as shown here.

B B B

B O A
O A O A O A

O O A O A
A B A

B
B B

The measure of rotation between the arms of an angle gives the measure of the angle in degrees
(°). A complete turn about a certain point is divided into 360 parts. Each part measures 1°, so a
complete turn around the fixed point measures 360°.

The measure of an angle is called its magnitude, which does not depend on the lengths of the arms
of the angle. Now, let us learn how to measure the magnitude of an angle.
A Pinch of History
Historical Perspective of Angle: Ancient people knew that a circular figure can be divided into 360
parts. This concept has been in practice during Vedic Period. In the Rigveda (1.164.48), the sloka speaks
of a wheel with 360 spokes.
rfLeu lkoaQ rfj'krk u 'kÄdoks-v£irk% "kf‘uZ pykpykl%AA
Tasmin sākaṃ triśatā na śaṅkavo.arpitāḥ ṣaṣṭirna calācalāsaḥ.

Stick Bhaskaracharya had designed a machine
known as Chakra Yantra, or disk machine, Stick
Chain which is a type of protractor used for angular Protractor
marking of land and angular positioning of
Disk cities.

The Chaapa (semicircle) Yantra of Bhaskaracharya was used for measuring vertical angles.
A clay tablet excavated at Shush in Iran in 1936 confirms that the Babylonians used to measure the
angles by dividing a circle into 360 parts. Babylonian and Egyptian calenders were based on 360 days in
a year. Due to the sexagesimal system of dividing 60 and 360; Babylonians used this system to measure
angles, time etc. Since 360 can be divided evenly into 1, 2, 3, 4, 5 ,6, 8, 9, 10, 12, 24 etc. parts conveniently;
mathematicians might have thought of 360° angle of a circle. The Babylonians knew that the perimeter
of a hexagon was exactly equal to six times the radius of a circumscribed circle, a fact that was the
reason they chose to divide a circle into 360 parts. As far as back 1500 BCE, Egyptians were the first to
measure the angles using the Sun’s shadow on the marked stone tablets with some degree of accuracy.

41 Lines and Angles