Page 48 - Ganit Kaushal

2.7 DEGREE MEASURE OF VARIOUS ANGLES

By now, we have understood the measurement of some standard angles like the straight angle and the right
angle, but the question arises, how can we measure other angles in degrees?
For this purpose, there is a tool called a protractor, which is usually a half circle divided into 180 equal parts
by short marks, each measuring 1° (see adjoining figure).
It is a must for your geometry box.

There are two sets of numbers on the protractor.
(a) Increasing (0° to 180°) from right to left, i.e., in the
anticlockwise sense of rotation (see section 2.8 for
sense of rotation). This is also called the inner circle
of the protractor.
(b) Increasing (0° to 180°) from left to right, i.e., in the
clockwise sense of rotation. This is the outer circle.
Starting from the 0 mark on the rightmost point of the baseline, there is a long mark for every 10°. In between
every two such long marks, there is a medium-sized mark after 5°. It can be seen in the given figure. The point
O is called the centre of the protractor.

To measure an angle, place the protractor so that the centre of the protractor is on the vertex of the angle. Now,
align the protractor on one of the arms of the angle that passes through the 0° mark on the baseline, shown
by the thick red ray OB in the given figure. Now, observe where the other arm (thick red ray OA in the given
figure) of the angle passes through the protractor.

Can you tell the degree measurement of ∠AOB in the figure given above?
Great! You got it right. It is 80°.
In a similar manner, we can measure any given angle with the help of a protractor.

Constructing Angles Using a Protractor

A protractor is a tool that is used not only to measure but also to construct an angle of a given measurement.
Suppose we want to construct an angle of measure 50°. We can easily construct it using a protractor by following
the steps given below.
We will take the help of the figure below to explain the procedure.

Step 1: Draw a ray OB.
Step 2: Now, place the protractor on ray OB such that its centre coincides with the initial point O and the
baseline lies along ray OB (See figure below).
Step 3: Mark a point A on the paper
along the long mark of 50° on the
inner circle.
Step 4: Remove the protractor, draw
the ray OA; the ∠BOA, so obtained
is the required angle of 50°.
Similarly, we can construct any given
angle with the help of a protractor.

46 Mathematics-6