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Large angles

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

Straight angle, reflex angle, full angle: you learn about large angles and measure and draw reflex angles.
📄 Open worksheet (PDF, German)

The video

In the video a reflex angle is measured with a helping line (die Hilfslinie) and drawn with \(360^\circ - \alpha\).

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

Contents of the video

  1. 0:00 Introduction
  2. 0:13 The straight angle
  3. 0:30 The reflex angle
  4. 0:44 Measuring reflex angles
  5. 1:24 Drawing reflex angles
  6. 2:13 The full angle
  7. 2:26 All types of angles
  8. 2:49 Try it yourself

The most important points

Large angles

straight (gestreckt): exactly \(180^\circ\) · reflex (überstumpf): between \(180^\circ\) and \(360^\circ\) · full angle (der Vollwinkel): exactly \(360^\circ\).

A straight angle: the arms form a line.
A straight angle: the arms form a line.

Measuring reflex angles

Extend the 1st arm past \(S\) (helping line): that is \(180^\circ\). Measure the rest with the set square and add: \(180^\circ + 55^\circ = 235^\circ\).

180^\circ + 55^\circ = 235^\circ
\(180^\circ + 55^\circ = 235^\circ\)

Drawing reflex angles

Calculate \(360^\circ - 235^\circ = 125^\circ\). Draw \(125^\circ\) below. The angle around the top is then \(235^\circ\).

125^\circ below, 235^\circ around the top.
\(125^\circ\) below, \(235^\circ\) around the top.

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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The worksheet – Page 4
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Show the worksheet solutions
The worksheet – Page 5
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Try it yourself

Task

Which type of angle? a) \(180^\circ\) b) \(250^\circ\) c) \(360^\circ\) d) \(170^\circ\)

Show solution

a) straight b) reflex c) full angle d) obtuse

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: large angles (gestreckt, überstumpf, Vollwinkel), measuring reflex angles (180 degrees plus rest) and drawing them (360 degrees minus the angle). 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.