Finding Angle at $\gamma$ - Help Requested

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Discussion Overview

The discussion revolves around determining the angle at $\gamma$ in a geometric context, specifically related to theorems applicable to angles formed by lines and circles. Participants are seeking clarification on the appropriate theorem to apply in this scenario.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant requests guidance on which theorem to use to find the angle at $\gamma$.
  • Some participants suggest using the vertical angles theorem to determine the angle.
  • Another participant expresses concern that the vertical angles theorem only provides the angle between two straight lines, implying that $\gamma$ may refer to a different angle related to a circle.
  • There is a reiteration that $\gamma$ should be considered as the angle between the two straight lines, which some participants agree with.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of angle $\gamma$ and the applicability of the vertical angles theorem, indicating that the discussion remains unresolved regarding the correct approach to find the angle.

Contextual Notes

There are assumptions about the definitions of angles and the context in which $\gamma$ is situated, which are not fully clarified. The discussion lacks a definitive resolution on how to approach the problem.

Carla1985
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Hi,

could someone please tell me what theorem I need to be looking at to work out the angle at $\gamma$ please? I've worked out the rest but can't find a theorem for this one.

Thanks
 

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Use the vertical angles theorem.
 
Euge said:
Use the vertical angles theorem.

Thanks but that just gives me the angle between the two straight lines. My impression was that $\gamma$ was the part of the angle up to the edge of the circle.
 
That would not make an angle, for an angle is formed by two straight lines. It would only make sense for $gamma$ to be the angle between those two lines.
 
Euge said:
That would not make an angle, for an angle is formed by two straight lines. It would only make sense for $gamma$ to be the angle between those two lines.

That would make things a whole lot easier. Thank you for your help!
 

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