Geometry Problem

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Level: High School, SAT Prep, College geometry

## Thursday, December 23, 2010

### Problem 554: Concave Quadrilateral, Angles, Sum

Labels:
angle,
concave,
quadrilateral

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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.