Simplifying Exterior Angles in a Polygon

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SUMMARY

This discussion focuses on simplifying the calculation of exterior angles in a polygon, specifically through the use of the relationship between interior and exterior angles. The key equations referenced include the sum of interior angles formula, (n-2)*180, and the property that the sum of angles in a quadrilateral equals 360 degrees. The solution process involves recognizing that angles forming a straight line sum to 180 degrees, allowing for straightforward calculations of unknown angles, such as x. The final conclusion is that x equals 80 degrees, derived from the equation 100 + x = 180.

PREREQUISITES
  • Understanding of polygon angle properties
  • Familiarity with basic algebraic equations
  • Knowledge of the relationship between interior and exterior angles
  • Ability to solve for unknown variables in equations
NEXT STEPS
  • Study the properties of polygons and their angles
  • Learn how to derive the sum of interior angles for different polygon types
  • Explore the concept of linear pairs of angles and their applications
  • Practice solving for unknown angles in various geometric configurations
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Students studying geometry, educators teaching angle relationships, and anyone looking to enhance their problem-solving skills in polygon-related mathematics.

Frank212
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Homework Statement


bandicam 2016-08-14 00-45-30-451.jpg


Homework Equations


sum interior angles (n-2)*180
angles of a quadrilateral: a+b+c=d = 360
[/B]

The Attempt at a Solution


What do you do with the exterior angle?
80+130+a+x=360
 
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Frank212 said:

Homework Statement


View attachment 104635

Homework Equations


sum interior angles (n-2)*180
angles of a quadrilateral: a+b+c=d = 360
[/B]

The Attempt at a Solution


What do you do with the exterior angle?
105+80+130+a+x=360

How would you find ##x## from the information in the diagram?
 
Ray Vickson said:
How would you find ##x## from the information in the diagram?
a+130+x=360
180-100=80
x=80
130+80+85= 295
360-295=65
a=65
 
Frank212 said:
a+130+x=360
180-100=80
x=80
130+80+85= 295
360-295=65
a=65

Much easier: just use the fact that 100+x = 180, because the angles 100 and x make up a straight line. (I know you got the correct value for x above, but I found your argument to be confusing and not as step-by-logical-step as it should be.)
 

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