What does Angle ABC Equal?

Date: 5 Mar 1995 13:07:10 -0500
From: Vivien Cumyn
Subject: Triangle problem

Ok, I've got a real whopper of a problem,

A triangle, ABC, is obtuse angled at C. The bisectors of the exterior 
angles at A and B meet BC and AC produced at D and E respectively. 
If AB =AD =BE, then angle ABC is equal to ?

Date: 5 Mar 1995 16:53:13 -0500
From: Dr. Ken
Subject: Re: Triangle problem

Hello there!

I'll see if I can give you a few hints, without actually solving the 
problem for you.

1) since AB = AD = BE, triangles DAB and ABE are isosceles, so 
   angle DBA = BDA, and angle EAB = AEB.

2) Draw your picture with AB horizontal and C below it.  Notice 
that there was no asymmetrical information in the problem, meaning 
that whatever we constructed on the left side we also constructed on 
the right side and vice versa.  So you can probably assume that angle 
CAB = CBA, which will greatly reduce the complexity of the 
calculations, since you can use the same variable to represent 
each of them.

See if you can tackle it now, with these things in mind.  If you can't,
write back and we'll help you out some more.

-Ken "Dr." Math