Triangle ABC is isosceles with AB=BC. There is a point D on AC such that BD = DC and AB=AD.

What is the measure of angle BAC?

Let:
Angle BAC = x = Angle BCA

Since Triangle BDC is also Isosceles - Angle DBC = x

Let:
Angle ABD = y

:. Angle ABC = x+y

Now :

x+y = 180-2x
&
x+2y = 180 ( By the angles ADB and BDC )

Which gives us --- y = 2x

Now since 3x+y = 180

X = 36

Posted by Syzygy on 2004-09-01 09:21:54