Geometry Problem
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Level: High School, SAT Prep, College geometry
Thursday, December 23, 2010
Problem 554: Concave Quadrilateral, Angles, Sum
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Geometry Problem
Click the figure below to see the complete problem 554.
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Level: High School, SAT Prep, College geometry
extend AD to E, E on BC
ReplyDeletex = DEC + c = a + b + c
Join points B and D.
ReplyDeleteConsider 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.
Join AC, <DAC+<DCA=180-x
ReplyDeletea+b+c+<DAC+<DCA=180
a+b+c=x