How to Use a Protractor to Measure and Draw Angles? Facile Tips

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How to Use a Protractor to Measure and Draw Angles

A protractor is an instrument used to measure or draw angles. Most protractors are either circular or semicircular, and are typically made of transparent plastic for better precision. Here are some step-by-step instructions, provided by ScienceStruck, on how to use a protractor.

Angle Types

  • Acute Angles: Measure less than 90°
  • Obtuse Angles: Measure more than 90°
  • Right Angles: Measure exactly 90°
  • Straight Angles: Measure 180°
  • Reflex Angles: Measure more than 180°

Most protractors measure angles in degrees, whereas a few also measure them in radians. The latter are popularly referred to as radian-scale protractors; and are used for complex, mechanical figures; especially in the field of engineering or architecture.

Protractors are widely used in schools to help students learn geometry. These are mostly semicircular, and can be used to draw or measure angles up to a maximum of 180°. If semicircular protractors measure angles up to 180°, how much can a circular protractor measure? Simple! 360°. However, a semicircular protractor is also capable of measuring angles up to 360°, even though it does not have the respective markings.

Let’s begin with learning to draw an angle using a protractor, and also learn how to measure already drawn angles. Additionally, we’ll also teach you to draw or measure angles more than 180° using a regular semicircular protractor. Take a look!

How to Use a Protractor to Draw an Angle

Drawing an angle using a protractor is very simple. All you need is a pencil, a sheet of paper (ruled/unruled), and a ruler (optional). Let’s start.

Draw a line

Draw a line segment (having two vertices) or ray (with one vertex). Do remember to properly mark the vertex upon which the proposed angle would be drawn. This will help you to easily spot it through the protractor.

Align protractor

Decide the degree of your angle. Once decided, place the protractor over the marked vertex, such that the protractor’s mid point and the vertex are aligned (refer to the illustration).

Place protractor

Once aligned, hold the protractor steady, and mark the desired angle with a point. To measure an angle you’ll have to begin with 0° (the angle of your line), and count upwards till you see the value of your desired angle. Most protractors have reversible readings, which means you can begin with zero on both sides.

However, in case there’s only one-way reading (from 0 to 180), and you wish to start from the higher side; treat 180 as 0, 170 as 10, 160 as 20, 150 as 30, and so on.

Complete angle

Once you have marked your desired angle, join the vertex (used to draw the angle), and the marked point. You could either achieve this by using a ruler or the straight edge of the protractor. That’s it! You’ve successfully drawn an angle using your protractor.

How to Use a Protractor to Measure an Angle

Measuring is even easier than drawing. Let’s see how.

Angle not measured

Place your protractor on the connecting vertex of a previously drawn angle.

Measure with protractor

Align the protractor to the base line such that it coincides with 0°. Then, mark the angle of the other line as per the reading on your protractor. Begin measuring from the base line to the angle line, and not from the other side.

Write the angle measure

Once you measure the angle, write the reading between the two lines (as shown in the illustration).

How to Draw Angles Exceeding 180° Using a Semicircular Protractor

Although drawing angles more than 180° using a regular semicircular protractor may seem like a tough job, it isn’t so. You can learn this in four simple steps. Here they are.

Begin by drawing a line such that you leave ample space at the top and bottom of the line. Then, mark a vertex, and measure 180° using your protractor.

Once measured, draw a dotted line from the vertex to the marked point.

Now flip the paper, and hold the protractor once again on the marked vertex. Considering the dotted line as your base line, and 0° as 180°, mark the desired angle. For instance, if you wish to draw an angle measuring 260°, begin counting from 180 to 260. So, 260° will be an additional 80° from 0.

After you’ve marked the said angle, draw a line connecting the vertex and the marked point. Then, flip the paper, and you have your desired angle exceeding 180° without using a circular protractor.

How to Measure Angles Exceeding 180° Using a Semicircular Protractor

Place the protractor on the vertex of the base line, and draw a dotted line for 180°.

Flip the paper, keep the protractor on the vertex, and measure from the dotted line to the angle line. Now, add the acquired angle to 180°. For example, if you counted 20° from the dotted line, the reflex angle measures 180 + 20 which is 200°.

This is how you can use a protractor to measure as well as draw angles, quickly and easily. Make good use of this guide and score good grades in geometry. Good luck!

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