ACED is an isosceles trapeziod.  Given the measure of two carefully chosen angles it is possible to find the measures of all the other angles in the figure.  This is one of my favorite problems, because the solution requires the use of three major theorems from Euclidean plane geometry.

Find the measures of the following twelve angles

ABD (given)
BEC (given)
ABC
CBE
EBD
BCE
BCA
CAB
BAD
ADB
BDE
DEB

Click HERE to find out the three theorems needed.