See complete Problem 214 at:
gogeometry.com/problem/p214_quadrilateral_angle_bisector.htm
Level: High School, SAT Prep, College geometry
Friday, January 2, 2009
Elearn Geometry Problem 214: Quadrilateral, Angle Bisectors
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BAC + CDA + ABC + DCB = 360 (1)
ReplyDeleteB/2 + C/2 + x = 180 (2)
B + C = 360 - 2x
B + C = 360 - A - D
then 360 - 2x = 360 - A - D
-2x = -A -D
x = (A-D)/2
1st mistake to the anonunous solution :
ReplyDeleteIn the 1st equation "BAC" should be replaced with BAD.
2nd mistake : if -2X=-A-D then 2X=A+D, so X=(A+D)/2 and not X=(A-D)/2.
Hoever his solution (with the above corrections) is right and elegant.
G. Platis