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Angle-bisectors

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Angle-bisectors

by 4meonly » Sun Nov 23, 2008 3:00 am
BE and CE are angle-bisectors of the angles CBD abd BCF respectively. If angle BAC =50 degrees, then find the angle BEC in degree measure.
A) 70
B) 55
C) 60
D) 65
E) 75

OA D

Semi-hard Q. Just interested in your approach.
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by raunekk » Sun Nov 23, 2008 4:32 am
Let AngleCBE = AngleDBE = y (BE is angle bisector)
let angleBCE = angleFCE = z (CE is angle bisector)

angleBAC = X = 50

Thus we can form an equation,
angleBAC+angleBCA+angle ABC = 180

angle ABC+y +y = 180

angle ABC = 180-2y
simillary,
angle ACB= 180 - 2z

Thus ,
180-2y+180-2z+50=180
2y+2z=230
y+z=115...(1)

Now triangleBCE
Let angle E be p
so,
angle CBE+angleBCE+CEB = 180
i.e, angle E +y + z = 180

(from 1,y +z = 115)
thus angle E = 180-115
=65
thusD

thanks.
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