Solve Quadrilateral Exterior Angles Sum Equal to Interior Angles Sum

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SUMMARY

The sum of the exterior angles at opposite vertices of any quadrilateral is equal to the sum of the interior angles at the other two vertices. This can be established using the formula for the interior angles of a quadrilateral, which is 360 degrees, and the relationship between adjacent interior and exterior angles. Specifically, if A and C are opposite angles, then the exterior angles A' and C' can be calculated, leading to a definitive conclusion that A' + C' equals the sum of the interior angles at the remaining vertices B and D.

PREREQUISITES
  • Understanding of basic geometry concepts, specifically quadrilaterals.
  • Familiarity with the properties of interior and exterior angles.
  • Knowledge of angle relationships, including adjacent and opposite angles.
  • Ability to apply algebraic manipulation to geometric formulas.
NEXT STEPS
  • Study the properties of quadrilaterals in Euclidean geometry.
  • Learn about the relationships between interior and exterior angles in polygons.
  • Explore proofs related to angle sums in various geometric shapes.
  • Investigate the implications of angle relationships in real-world applications, such as architecture and design.
USEFUL FOR

Students studying geometry, educators teaching angle relationships, and anyone interested in understanding the properties of quadrilaterals and their angles.

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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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