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How to Measure Angles

This is the complimentary worksheet for this tutorial. Below are seven different exercises for you to

work through, followed by the worked-through solutions. You'll need a protractor for these exercises.

Measure each of the below angles. For extra points, try to also name them (related tutorial here).

Exercise 1.

Exercise 2.

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Exercise 3.

Exercise 4.

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Exercise 5.

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Exercise 6.

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Exercise 7.

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Answers

Exercise 1.

This angle is 135 degrees. This is an obtuse angle because it is between 91 and 180 degrees.

Exercise 2.

This is also 135 degrees. You need to use the inner circle of numbers to measure the angle, because it is

measured anti-clockwise. Why? Because we're using the zero horizontal line on the left hand side of the

centre of the protractor.

Another method of measuring the angle is to measure the smaller angle on the right hand side, from the

0 degree line, and subtract it from 180 degrees (as shown on next page).

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i.e. 180 - 45 = 135 degrees. The 135 degree angle is another obtuse angle because it is between 91 and

180 degrees. The 45 degree angle is an acute angle between it is less than 90 degrees.

Exercise 3.

This angle is 100 degrees and is an obtuse angle because it is between 91 and 180 degrees.

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Exercise 4.

This is a 60 degree angle. Like Exercise 2, you need to use the inner circle of numbers to measure the

angle (once again we're measuring anti-clockwise). Also like Exercise 2, you can also do it by measuring

the angle on the right hand side, and subtracting it from 180 degrees.

i.e. 180 - 120 = 60 degrees (as shown below). The 60 degree angle is an acute angle, because it is less

than 90 degrees. The 120 degree angle is an obtuse one because it is between 91 and 180 degrees.

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Exercise 5 .

This is a 30 degree angle. It is an acute angle because it is less than 90 degrees.

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Exercise 6.

A full protractor has been used for this exercise, but a semi-circle protractor would work just as well.

Notice how the protractor has been turned to ensure one arm is sitting on the zero mark? This angle

measures 160 degrees; it is an obtuse angle because it is between 91 and 180 degrees.

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Exercise 7.

This angle is 300 degrees. It is a reflex angle because it is between 181 and 359 degrees.