How to Measure an Angle Using a Protractor

Last Updated: December 22, 2022 References

A protractor is a handy tool that allows you to precisely measure the number of degrees in any angle. The typical protractor is made of clear plastic and has two sets of numbers around the edge. The numbers you use depend on whether the angle you're measuring is acute (less than 90 degrees) or obtuse (more than 90 degrees but less than 180). If you're dealing with a reflex angle (more than 180 degrees but less than 360), you'll have to do an additional calculation.^{[1]
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Method 1

Method 1 of 2:

Measuring Acute and Obtuse Angles

1
Determine what type of angle you're measuring. A right angle is exactly 90 degrees. If an angle is less than 90 degrees, it's an acute angle. Obtuse angles, on the other hand, are more than 90 degrees but fewer than 180.^{[2]
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- In some diagrams, you may see more than one angle. The arc around the vertex shows you which angle you're supposed to find the value of.
- Labeling an angle acute or obtuse helps you reading the protractor. For example, if you know you have an obtuse angle, then you know it is going to be more than 90 degrees. If you get a smaller number from your protractor, you're likely looking at the wrong scale.
2
Place the center of your protractor on the vertex of the angle. At the bottom of your protractor, you'll see a little hole in the center. Typically this hole has vertical and horizontal lines crossing it, so you can line up the protractor exactly.^{[3]
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- To make sure you're right on the vertex, it can help to make a little dot inside the center of your protractor. Then remove your protractor and confirm the dot is on the exact tip of the vertex.
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3
Line up one line with the protractor's baseline. The baseline of your protractor is the solid line on the bottom with a "0" at either end. Once you have the protractor on the vertex of the angle, adjust either the protractor itself or your paper until one line is following the baseline.^{[4]
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- If one line is more horizontal, it will typically be the easiest one to line up along the baseline. However, you'll get the same result no matter which line you use.^{[5]
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4
Find the degrees in the angle using the correct scale. Along the outside of the protractor are 2 arcs of numbers. Use the outer arc if the angle you're measuring opens to the left. Use the inner arc if the angle you're measuring opens to the right. The number that the other line of the angle crosses is the number of degrees in that angle.^{[6]
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- Protractors usually provide numbers in 10s. If the angle you're measuring doesn't line up perfectly with a number, count the hash marks on the outside edge of the protractor to determine the degrees in that angle.
Tip: To visualize whether the angle opens to the right or the left, imagine the angle rays are an alligator's jaws. No matter how wide, the direction the alligator is pointing when its "jaws" are closed is the direction the angle opens.

Method 2

Method 2 of 2:

Calculating Reflex Angles

1
Draw a straight line from the vertex of the angle. Line up the straight edge of your protractor under the horizontal line of the angle. Extend the line straight out from the vertex across the other side.^{[7]
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- If you look below the straight line, you'll see another angle. This smaller acute angle is formed by the straight line you drew and the diagonal line of the original reflex angle.
2
Place your protractor on the straight line to measure the acute angle. Line up the horizontal line on the baseline of your protractor, placing the center of your protractor over the vertex. Look where the diagonal line crosses the protractor to determine the number of degrees in the acute angle.^{[8]
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- You may find it easier to measure if you turn your paper so that the acute angle is facing straight up.
3
Add the measurement of the acute angle and 180. A reflex angle is more than 180 degrees, but less than 360. The acute angle you just measured plus 180 degrees will give you the degrees in the reflex angle.^{[9]
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- For example, if the reflex angle produces an acute angle of 18 degrees, that would mean the reflex angle is 198 degrees.
Variation: There are full-circle protractors that eliminate the need for this additional math.

Community Q&A

Question

How do I know which arc to use when measuring any angles?

Donagan

Top Answerer

The arcs are identical in terms of angular measurement. One arc begins with 0° on the right side. The other arc begins with 0° on the left side. Use the arc that allows you to measure an angle in the direction you prefer: clockwise or counter/anticlockwise.