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# Using a Protractor

Measuring angles with a protractor can be a confusing experience. There are many things to which you must pay attention. Understanding that angles are parts of circles is helpful, because then the design of the protractor makes sense. With a little practice, you will soon be measuring angles with ease.

## What is a protractor?

A protractor is a measuring tool often made of translucent plastic or glass used to read, measure, and construct angles. The most common protractor is a semicircle-shaped scale ranging from 0° to 180°.

Protractors can have diameters ranging from two inches to more than twelve inches. They are typically made of brass, steel, wood, ivory, or plastic.

Angles are typically measured in degrees (°). More so, most protractors have 180 equal segments. However, some protractors are in radian or arcminute scale.

## What is the origin of protractors?

The use of protractors dates back over 500 years. Although older instruments were used for angle measurement in addition to other mathematical pursuits, Thomas Blundeville introduced a tool specifically for measuring and constructing angles in his 1589 Briefe Description of Universal Mappes & Cardes. It is unclear whether Blundeville developed the protractor. However, it was written in his book that he used the protractor to create maps, particularly for nautical charts.

In the early 17th century, protractors were widely used by navigators and surveyors. Meanwhile, in 1810, Joseph Huddart, a US naval commander, produced a more advanced version of a protractor created to plot a ship’s position on a nautical chart. It was then called as a three-arm protractor. By the nineteenth century, machinists had developed a wide range of specialized protractors. Then in the 20th century, protractors had also become ubiquitous in school mathematics.

### Warm Up

Recall what you have learned about angles already. Angles are sections of a full circle. Since a full circle measures 360º, an individual angle has to measure less than 360º, because it is part of a circle.

Estimating the approximate measurement of a circle before you actually measure it can be helpful. By comparing your actual answer to your estimated measurement, you can determine whether or not your answer is reasonable.

In this lesson you will estimate angle measurements, find actual measurements using a protractor, and draw angles of various sizes.

## How to use a protractor?

Protractors can be used to read and measure different angles. Now, this section will help you understand how to properly use a protractor.

A protractor can be used to read angles by using its either inner or outer readings. The inner and outer reading of each angle is always a supplement of each other since the sum of it will always be 180°.

Now, here’s how we can read angles using a protractor.

1. Place the center of the protractor to the vertex of any angle.
2. Place the protractor’s baseline on the ray, which is the angle’s base.
3. Determine if you will use the inner or outer reading. If the angle to be measured is on the left-hand side of the protractor’s center, then we need to use the outer reading. If the angle is formed on the right-hand side of the protractor’s center, use the inner reading.

Example #1

Using a protractor, read the angle given in the figure.

Solution

Example #2

Read the angle on a protractor.

Solution

Example #3

Read the angles on the protractor.

Solution

### Measuring angles using a protractor

To measure an angle using a protractor, you may consider following the steps below:

1. Align the vertex of the angle on the midpoint of the protractor (usually a dot indicates the midpoint of the protractor).
2. Align one side of the angle with 0 degrees on the protractor.
3. Check where the other side of the angle intersects the number scale – that will determine the measure of the angle.

Make sure you’re reading from the correct set of numbers as most protractors have two sets of numbers: one from 0° to 180° and another from 180° to 0°.

Example

Using a protractor, measure the given angle.

Solution

## How to construct angles using a protractor?

To construct angles using a protractor, use the following steps:

1. Draw the base of the angle.
2. Make sure to align the baseline of the protractor to the base of the angle such that the protractor’s center is placed on the vertex of the angle.
3. Put a mark to the measure of the angle that you want to create.
4. Draw a line by connecting the vertex of the angle to the dot that you made from step 3.

## Main Lesson: Using a Protractor

Now it’s time to talk about the tool that is used to measure angles. You may have wondered why it is shaped the way it is. Knowing that angles are measured by how many degrees of a circle are between the two rays, the shape starts to make more sense.

Help your children see the similarities between a half circle and the protractor. Show them that two protractors with the straight edges together would form a whole circle. Point out the similarities between the measurement markings and a regular ruler.

Line up the endpoint of the rays, called the vertex of the angle, with the crossed lines in the middle of the straight edge on the protractor. Line up the line that points to zero lined up with one of the rays that make the angle. Use the ruler on the curved edge to count the degrees until you reach the other ray in the angle.

Now that you understand how a protractor works, let’s look at a couple of angles and measure them:

Whatever number of one-degree curves is an angle, that number equals the measurement of the angle.

Remind your children that it is very important to line up the protractor correctly so they can get a correct measurement. The crossed lines at the bottom of the straight edge must be matched up with the vertex (endpoint) where the two rays are joined.

## Drawing Angles

A protractor can also be used to draw angles.

Example #1

Construct an acute angle using a protractor.

Solution

Example #2

Using a protractor, construct an angle that measures 150°.

Solution

## What are the different kinds of protractors?

There are different kinds of protractors that can also be used for different purposes.

### Typical Protractor

The most typical and standard protractor is shaped as a half-circle that can measure 0° to 180°.

### 360° Protractor

A 360° protractor is designed as a whole circle wherein the readings are from 0° to 360°. This can be used to construct and measure reflex angles. More so, it provides more precision when measuring angles. It is often used in mechanical drawings, architecture, and even in meteorology.

### Bevel Protractor

A bevel protractor is a graduated circular protractor made up of a beam, a dial, with one pivoting arm that is used to measure or mark off angles. Vernier scales are sometimes used to provide more exact readings. It is mostly used in architectural or mechanical drawing. However, since there is already modern software for drawing like CAD, the use of it is declining.

### Protractors Through Time

The table shows some kinds of protractors that are used through time.

## What is the importance of using a protractor?

In Geometry, a protractor allows us to measure and determine the names of different angles. Different kinds of protractors are also used in various fields such as architecture, engineering, and meteorology.

### Recap

• Angles are sections of a circle.
• Angles are measured in degrees.
• There are 360° in a circle.
• Individual angles measure less than 360°
• A protractor is used to measure angles.
• A protractor can also be used to draw an angle.
• It is important to line up the protractor correctly.