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Angles at lines

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

You learn adjacent, vertical, corresponding and alternate angles. You measure one angle and calculate the others.
📄 Open worksheet (PDF, German)

The video

In the video two lines cross. One angle is turned, another one is slid: this shows you which angles are equal.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:15 Adjacent angles
  3. 0:43 Vertical angles
  4. 1:04 Corresponding angles
  5. 1:32 Alternate angles
  6. 2:01 Finding all angles
  7. 2:27 Careful, mistake!
  8. 2:47 Try it yourself

The most important points

Adjacent and vertical angles

Adjacent angles (die Nebenwinkel) lie next to each other and together form a straight line: \(\alpha + \beta = 180^\circ\). Vertical angles (die Scheitelwinkel) are opposite each other and equal: \(\gamma = \alpha\) and \(\delta = \beta\).

Two lines cross: \alpha = 50^\circ, so \beta = 180^\circ - 50^\circ = 130^\circ.
Two lines cross: \(\alpha = 50^\circ\), so \(\beta = 180^\circ - 50^\circ = 130^\circ\).

Corresponding and alternate angles

Two parallel lines \(g \parallel h\) are crossed by a line \(t\). Corresponding angles (die Stufenwinkel, F-shape) are equal. Alternate angles (die Wechselwinkel, Z-shape) are equal too.

Corresponding angles: the angle is slid down along t and fits exactly.
Corresponding angles: the angle is slid down along \(t\) and fits exactly.

This is only true if the lines are parallel. From one measured angle you calculate all eight: four times \(60^\circ\) and four times \(120^\circ\).

Mistake: g and h are not parallel. The corresponding angles are 60^\circ and 45^\circ.
Mistake: \(g\) and \(h\) are not parallel. The corresponding angles are \(60^\circ\) and \(45^\circ\).

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
The worksheet – Page 4
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Try it yourself

Task

\(g \parallel h\). One angle is \(65^\circ\). How big are the other seven angles?

Show solution

Four times \(65^\circ\) and four times \(115^\circ\) (\(180^\circ - 65^\circ = 115^\circ\)).

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: Winkel an Geraden (Nebenwinkel, Scheitelwinkel, Stufenwinkel, Wechselwinkel, parallele Geraden). 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.