Thursday, December 23, 2010

Problem 554: Concave Quadrilateral, Angles, Sum

Geometry Problem
Click the figure below to see the complete problem 554.

 Problem 554: Quadrilateral, Angles, Sum.
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Level: High School, SAT Prep, College geometry

2 comments:

  1. extend AD to E, E on BC
    x = DEC + c = a + b + c

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  2. Join points B and D.
    Consider point E on line BD such that B-D-E.
    Let measure angle ABE = z
    hence, measure angle EBC= b-z
    By Exterior Angle Theorem,
    measure angle ADE= a+z
    measure angle CDE= c+(b-z)
    measure angle ADC = measure angle ADE + measure angle CDE...(angle addition postulate)
    Hence,x=[a+z]+[c+(b-z)]
    x=a+z+c+b-z
    x=a+b+c.

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