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

Labels:
angle,
angle bisector,
quadrilateral,
triangle

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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