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 360^o. 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 180^o. 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.

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.

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.

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

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.

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.

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.

And we have ∠CAB = 55^o 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.

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

Related Articles

• Geometric Tools
• Lines and Angles
• Supplementary and Complementary Angles
• Types of angles
• Degree and Radian

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.

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

Example 2:

Draw an angle of measure 60^o using a protractor.

Solution:

Let ∠AOB = 60^o, 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 60^O

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

We have ∠AOB = 60^o.

Example 3:

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

Solution:

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

Practice Questions

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