Protractor in geometry

A Protractor is a tool found in a geometry box usually made of plastic and used to measure angles. The protractor is also used to draw angles of given measures in degrees. There are different types of protractors that serve different purposes, such as a circular protractor which can measure angles up to 360o. Then, there is Bevel protractor which is a circular protractor attached to an arm so that the protractor can move about the joint, it is mainly used for architectural designing.

What is a Protractor?

A protractor in geometry is generally in the shape of a semi-circle which is divided into 180 equal parts and each part measures one degree. Hence, the ordinary protractor in a geometry box measures angles up to 180o. Protractors that we find in our geometry box are generally made of plastic but they are also made of wood, steel and in some cases glass. Most protractors measure the angle in degrees but there are few protractors available that can measure angles in radian, they are known as Radian-scale protractors.

Protractor

Table of Contents:

How to Use a Protractor to Measure an Angle

Let us see step by step how to measure an angle using a protractor,

Step 1: Suppose an angle given ∠AOB, whose measure we need to find out. Place the zero of the protractor accurately on the vertex of the given angle and the base arm of the angle coinciding with the zero degrees line of the protractor.

Angle using Protractor

Measuring angle with a protractor

Step 2: After placing the protractor accurately, we read the measure of the angle, since we are measuring in anticlockwise, we will read the inner calibration.

Measuring angle with a protractor

Step 3: Now, observe carefully and note down marking. So, the measure of ∠AOB = 60o

How to Use a Protractor to Draw an Angle

Let us see step by step how to draw an angle using a protractor,

Step 1: Draw a line segment AB using a ruler.

Line segment

Step 2: Now place the protractor on one of the ends of the line segment AB such that the end of line segment coincides with zero of the protractor and the base of the protractor coincide with the line segment. Mark the point of whichever degree angle you want to make.

Drawing angle with the help of a protractor

Step 3: Now remove the protractor and join the marked point to point A of the line segment with the help of a ruler and pencil.

Drawing angle

And we have ∠CAB = 55o drawn with the help of a protractor.

Some Important Points Related to Protractors

  • The angle we measure with the ordinary protractor in a geometry box is in degrees (o).
  • Whenever we are measuring angle in the anticlockwise direction we read the inner calibration of the protractor while measuring the angle in a clockwise direction we read the outer calibration of the protractor.

Calibration of a protractor

  • The inner and outer calibration of the protractor is the measure of supplementary angles, that is, they add up to 180o.

Measuring Supplementary angles using protractor

Related Articles

Solved Examples on Protractor

Example 1:

With the help of a protractor, find the measure of each angle of an equilateral triangle.

Solution:

Let △ABC be an equilateral triangle such that AB = BC = CA. Place the protractor over one of the vertices of the triangle.

Measuring angles of an Equilateral triangle using protractor

Repeat the same with each of the angles. We have each angle of an equilateral triangle is of 60o.

Example 2:

Draw an angle of measure 60o using a protractor.

Solution:

Let ∠AOB = 60o, the steps of construction :

(i) Draw a line segment OB with the help of a ruler

(ii) Keeping the protractor at O, mark a point A corresponding to 60O

Drawing angle using protractor

(iii) Join points O and A with the help of a ruler

Drawing angle

We have ∠AOB = 60o.

Example 3:

Use a protractor, find the measure of ∠CAB and find its supplementary angle.

Angle

Solution:

Using a protractor, measure ∠CAB = 75o and its supplementary angle is 105o.

Measuring angles using protractor

Practice Questions

1. Draw a 115o angle using a protractor.
2. Draw a sector of a circle with an angle of 120o using a protractor.
3. Draw an 89o angle and find its supplementary angle using a protractor.

Frequently Asked Questions (FAQs on Protractor)

Q1

What is a protractor in geometry?

A protractor is a tool that is used to measure and draw angles in geometry. A protractor in a geometry box is in the shape of half-disc or semicircular which can measure up to 180
degrees.

Q2

What is the main use of a protractor?

A protractor is used for measuring and drawing angles.

Q3

Is it necessary to have a protractor for geometry?

A protractor is used to measure and draw angles but alternatively, we can draw certain
angles with the help of compasses and measure them by applying certain geometrical properties.

Q4

How do we measure angles using a protractor?

Put the zero of the protractor coinciding with the vertex of the angle, also make sure that the
base arm of the angle is in line with the baseline or zero degrees line of the protractor. Now note the measure of the angle carefully.

Q5

What are the two uses of a protractor?

Protractors are used by architects to measure angles while designing any structure. Military protractors are used to determine the accurate direction by measuring the angle.

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