Protractor

A protractor is a simple measuring instrument that is used to measure angles. A common protractor is in the shape of a semicircle with an inner scale and an outer scale and with markings from 0° to 180° on it. Architects and designers use a more precise protractor called an angle protractor tool which gives more accurate measures. Protractors have been in use since the seventeenth century. Later by the eighteenth century, protractors were widely used in geometry and mathematics.

Protractor, in math, is considered to be an important measuring instrument that is in the shape of a semi-circle. The common protractor is a translucent tool that helps us measure angles in degrees. A radian scale protractor measures an angle in radians. If we observe the figure given below, we can see that a common protractor has degrees marked clockwise from 0° to 180° in the outer scale and anti-clockwise from 0° to 180° in the inner scale.

A protractor is an instrument which is very easy to use. It has two readings - the outer reading and the inner reading that help to measure a given angle.

How to Read a Protractor?

A protractor can be read using its inner readings or its outer readings depending on the angle that is formed. Each inner reading and outer reading supplements each other, i.e., they add up to 180°. For example, 0° + 180° = 180°, 10° + 170° = 180°, and so on. Observe the following figure to know how to read a protractor and relate to the steps given below.

• Step 1: We first need to pIace the center (hole) of the protractor on the vertex O.
• Step 2: Place the baseline of the protractor on the ray which is the base of the angle.
• Step 3: Decide which readings are to be followed. If the angle to be measured is formed on the left-hand side from the center of the protractor, we need to use the outer reading of the protractor. In this case ∠AOC = 60°.
• Step 4: If the angle to be measured is formed on the right-hand side from the center of the protractor, we need to use the inner readings of the protractor. In this case, ∠BOC = 120°.

For measuring angles with a protractor, let us use the following steps and relate to the figure given below.

• Step 1: In order to measure the angle ∠BOC, align the baseline of the protractor with the line AB such that the center circle of the protractor is at the vertex O.
• Step 2: Since the angle is formed on the right-hand side of the center, we will use the inner readings which go anti-clockwise.
• Step 3: Now, identify the reading on the protractor where ray C is extending. This shows that ∠BOC = 30°.

Now, let us find the measure of ∠AOC using the following steps.

• Step 1: Place the baseline of the protractor on line AO such that the centre of the protractor is placed on vertex O. Since we need to measure ∠AOC, which is formed on the left-hand side of the center, we will use the outer readings which go clockwise.
• Step 2: Check the reading where the ray OC is formed. It shows 150° on the outer scale.
• Step 3: Therefore, ∠AOC = 150º.

It should be noted that ∠AOC + ∠BOC form a straight line and hence add up to 180. This can be verified by the values, that is, 150º + 30º = 180º.

In order to draw angles using a protractor, we use the following steps. Let us see how to draw an angle of 40º using a protractor.

• Step 1: Draw a baseline AB.
• Step 2: Align the baseline of the protractor on AB such that the center of the protractor is placed on point A.
• Step 3: Since the angle is drawn on the right-hand side of the vertex we will see the inner readings.
• Step 4: In the inner readings, look for 40º and mark it as point C.
• Step 5: Now using a scale, join A and C. Therefore, ∠CAB = 40°.

360° Protractor

A 360° protractor is circular in shape and has readings up to 360° in the clockwise direction. It is commonly used in the field of architecture, mechanical drawings, and meteorology.

Important Notes

• We can also use a 360° protractor to draw a reflex angle. The angle protractor tool and 360° protractor give more precise measurements.
• If the angle to be measured is on the left-hand side from the center of the protractor, we use the outer readings of the protractor and if the angle to be measured is on the right-hand side of the center, we use the inner readings.
• To reduce errors, align the baseline and vertex properly.

☛ Related Articles

• 180 Degree Angle
• 30 Degree Angle
• Central Angle

What is a Protractor in Geometry?

A protractor is a simple measuring instrument that is used to measure or draw angles in degrees. A common protractor is in the shape of a semicircle that has an inner and an outer scale with markings from 0° to 180° on it.

How to Use a Protractor to Draw Angles?

A protractor can be used to measure and draw angles. The following steps can be used to draw angles using a protractor. For example, let us draw ∠COB = 50°.

• Step 1: Draw a baseline OB.
• Step 2: Mark the point O and place the center of the protractor at O.
• Step 3: Align the baseline of the protractor with the line OB.
• Step 4: Since the angle is to be formed on the right-hand side of the protractor, we will use the inner readings and look for 50°.
• Step 5: Mark a point C at 50° and join O to C. Hence, the required angle ∠COB = 50°.

What is the Shape of a Protractor?

The common protractor which is used in geometry is in the shape of a semicircle with markings of angles from 0° to 180° on it. There are other protractors that are circular in shape which can measure complete 360-degree angles. They are known as 360-degree protractors or full circle protractors.

How to Measure Angles with a Protractor?

A protractor is used to measure and draw angles. It can be read using its inner readings or its outer readings depending on the angle that is formed. For example, if we need to measure an angle using a protractor, we use the following steps.

• Step 1: Place the center (hole) of the protractor on the vertex and place the baseline of the protractor on the ray which is the base of the angle.
• Step 2: Decide which readings are to be followed. If the angle to be measured is formed on the left-hand side from the center of the protractor, we need to use the outer reading of the protractor.
• Step 3: If the angle to be measured is formed on the right-hand side from the center of the protractor, we need to use the inner readings of the protractor.

What is a Protractor Used for?

A common protractor, in geometry, is used to measure and draw angles from 0° to 180°. There are other protractors like the 360° protractor which is mostly used in the field of architecture, mechanical drawings, and in meteorology; there are other protractors like military protractors and bevel protractors that have other uses.

How to Use a 360 Degree Protractor?

A 360-degree protractor is circular in shape, has readings up to 360° in the clockwise direction and it can be used to draw and measure angles. The following steps show how to measure angles.

• Step 1: Place the center of the 360-degree protractor on the vertex.
• Step 2: The 0-degree line should be aligned with the baseline of the angle to be measured.
• Step 3: Observe the number on the 360-degree protractor where the other ray is pointing and take the readings.

What is a Triangle Protractor Called?

A triangle protractor is called a nautical protractor which is used by seamen for navigational charts. The markings of 45° angled lines make the access of 45, 90, and 135 easier for them.

What is a Bevel Protractor?

A bevel protractor is a graduated spherical protractor which has a pivoted arm used for marking angles. It is mostly used for mechanical and architectural drawings.