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Mathematics · Angles and geometry

Types of angle

Acute, right, obtuse, straight and full angles: learn to classify angles by their measure, test for a right angle with the corner of a sheet of paper, and find out why a rotated right angle is still a right angle.

  • 15 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

Looking at a map of his neighbourhood, Ahmet notices something: some streets cross each other exactly like a plus sign, while others meet at a sharp point. Turning his bike round the sharp corners is harder. Do you think we can sort the angles where streets meet into types? Which type of angle makes turning harder?

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

An obtuse angle: 120°

Turn the arm to set the angle. The angle goes up in steps of 5 degrees; when you reach the right value, press Check.

Prediction

Predict first

What type do you think the angle between the hour hand and the minute hand is at 4 o'clock?

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

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Paste this code into the HTML of your blog or school site. Visitors try the simulation without an account; no progress is saved.

The embedded page sets no cookies and does no tracking. A small link back to Kuazara sits underneath.

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Frequently asked

5 questions

Is a tilted corner still a right angle?

Yes. "Right" does not describe which way the angle faces; it means the two arms are perpendicular. If you turn a sheet of paper on the desk, its corner is still 90°. The type of an angle depends only on its measure, not on its direction on the page.

Is an angle with longer arms a bigger angle?

No. An angle measures the amount of turn between its two arms, not how long the arms are. A 120° angle drawn with short arms is still obtuse, and a 30° angle with very long arms is still acute.

Is exactly 90° acute or obtuse?

Neither; exactly 90° is a right angle. An acute angle is less than 90°, and an obtuse angle is between 90° and 180°. So 89° is acute and 91° is obtuse.

How can a straight angle or a full angle be an angle?

In a straight angle the arms lie on the same line and point in opposite directions: half a turn, or 180°. The hands of a clock at 6 o'clock look like this. In a full angle the arms lie on top of each other, but a whole turn, 360°, has been made between them.

How can I tell the type of an angle without a protractor?

Use the corner of a sheet of paper as a right-angle checker. Put the corner on the vertex of the angle and line up one arm with the edge of the paper. If the other arm stays inside the paper the angle is acute, if it lies on the edge it is right, and if it falls outside it is obtuse.