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Measuring angles

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

An angle has a vertex and two arms. You measure angles with the set square and learn about acute, right and obtuse angles.
📄 Open worksheet (PDF, German)

The video

In the video the set square measures angles in both directions. The right scale and the angle light up in pink.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:16 What is an angle?
  3. 0:50 Anticlockwise
  4. 1:17 Clockwise
  5. 2:06 Types of angles
  6. 2:27 Estimate first
  7. 3:20 Careful, mistake!
  8. 3:40 Try it yourself

The most important points

An angle has a vertex (der Scheitelpunkt) \(S\) and two arms (die Schenkel). The angle lies between the arms. Angles often have Greek letters as names: \(\alpha\) (alpha), \(\beta\) (beta).

From the 1st arm to the 2nd arm we turn anticlockwise here.
From the 1st arm to the 2nd arm we turn anticlockwise here.

Measuring an angle

Put the zero point exactly on \(S\) and the drawing edge on the 1st arm. Take the scale that starts with 0 at the 1st arm: 1st arm to the right – outer scale, 1st arm to the left – inner scale.

The 1st arm points to the left: we read 70^\circ on the inner scale.
The 1st arm points to the left: we read \(70^\circ\) on the inner scale.

Types of angles

acute (spitz): smaller than \(90^\circ\) · right (recht): exactly \(90^\circ\) · obtuse (stumpf): bigger than \(90^\circ\) and smaller than \(180^\circ\). Tip: estimate first, then measure – then you never take the wrong number.

An acute, a right and an obtuse angle.
An acute, a right and an obtuse angle.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
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Try it yourself

Task

Acute, right or obtuse? a) \(25^\circ\) b) \(90^\circ\) c) \(160^\circ\) d) \(89^\circ\)

Show solution

a) acute b) right c) obtuse d) acute

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: measuring angles with the set square (Scheitelpunkt, Schenkel, outer and inner scale) and types of angles (spitz, recht, stumpf). Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Use simple German sentences.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.