Solve Quadrilateral Exterior Angles Sum Equal to Interior Angles Sum

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Discussion Overview

The discussion revolves around proving a relationship between the sums of exterior angles at opposite vertices of a quadrilateral and the sums of interior angles at the other two vertices. The scope includes mathematical reasoning and exploration of geometric properties.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses frustration with the problem and attempts to reference formulas for the sums of interior and exterior angles.
  • Another participant suggests labeling the interior angles A, B, C, and D and questions the implications of subtracting the exterior angles from opposite vertices.
  • A participant confirms that the sum of the interior angles A, B, C, and D equals 360 degrees.
  • Another participant proposes a method involving adjacent angles and their relationships to derive the sums of the exterior angles.
  • One participant expresses confusion about the discussion and the steps being taken.
  • A later reply reiterates the known sum of the interior angles and prompts consideration of the exterior angles corresponding to two opposite angles.

Areas of Agreement / Disagreement

Participants generally acknowledge that the sum of the interior angles of a quadrilateral is 360 degrees, but the discussion remains unresolved regarding the proof of the relationship between the sums of exterior and interior angles.

Contextual Notes

Some participants appear to be struggling with the mathematical steps and relationships involved in the proof, indicating potential gaps in understanding or missing assumptions.

thomasrules
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Prove that the sum of the exterior angles at opposite vertices of any quadrilateral es equal to the sum of the interior angles at the other two vertices.

THIS question is REAly really really really getting me frustrated...

The way we're suppost to do it is like this...

180n-360 is the interior angles and exterior angles is 180n-180(n-2)

From there I don't know...
 
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The four interior angles are labeled A, B, C, and D, and you know the sum of these. What happens if you subtract the exterior angles from opposite vertices?
 
I don't know man I'm frigging confused...

so you saying that A+B+C+D=360?
 
If A and A' are two adjacent angles, then A + A' = 180deg.
Similarly for C and C'. Now find A' + C' wrt A and C. Then find B + D wrt A and C.
 
i'm lost :(
 
You already know A+B+C+D=360, right?. Now take two opposite angles (assume A and C). What is the sum of the exterior angles of these 2?
 

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