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Mathematics · Angles and geometry

What is an angle and how do you measure it?

Does the size of an angle depend on the length of its arms or on how far it turns? Learn the parts of an angle, the degree as a unit, and how to measure accurately with a protractor, using clocks and skateboards as examples.

  • 15 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

The clock on the wall shows exactly 3 o'clock. The hour hand is on 3, the minute hand is on 12, and there is an "opening" between them. As the time moves towards 6, that opening gets wider. So how do we measure it? Can we put a number on how steep a ramp in the skate park is, or on the angle at which a footballer strikes the ball?

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Protractor

Make a 70-degree angle

Turn the arm using the slider or the preset buttons. When you have set the angle, press Check.

Prediction

Predict first

How do you think a 70° angle looks compared with a right angle (90°)?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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Frequently asked

5 questions

What is an angle?

An angle is the shape made by two rays that start from the same point. The shared point is the vertex and the rays are the arms. The size of the angle shows how far one arm is turned from the other.

How many degrees are in a full turn?

A full turn is 360 degrees. A half turn is 180 degrees and a quarter turn is 90 degrees; an angle of 90 degrees is called a right angle.

If I make the arms longer, does the angle get bigger?

No. The size of an angle depends on the amount of turn between the arms, not on how long they are. At 3 o'clock the hands of a large wall clock and of a small wristwatch both make an angle of 90 degrees.

How do I measure correctly with a protractor?

Put the centre of the protractor on the vertex and line up the 0 line with one arm. Read where the other arm crosses, using the scale that starts at 0. Check the result by eye: an angle that looks sharp must be less than 90 degrees.

Why is a full turn 360 degrees?

Nobody knows the exact origin. Common explanations point to the Babylonians' base-60 number system and to the fact that 360 divides evenly by many numbers, such as 2, 3, 4, 5, 6, 8, 9, 10 and 12, which makes angles easy to share out.