Locate point E so that triangle EAB is congruent to triangle DAC
Extend BC to F so that CF = CD. Draw DF
I won't go through every step. I'll just tell you enough so
you can write it out like your teacher wants you to.
Using the fact that isosceles triangles have equal
base angles, that interior angles of a triangle have sum 180°,
that supplementary angles have sum 180°, and that vertical angles
are equal, you can now write the number of degrees in every
angle in the figure. That would be a good idea.
Therefore it is easy to show that
angle EAD = 100° = angle ADC = angle AEB.
Then by SAS, triangles ADC, AEB and AED are all congruent. So
AB = ED.
It is easy to show that angle DCF = 60° and that triangle CFD is
equilateral. You then show that BFDE is a parallelogram because
angle F = 60° = angle BED , angle EBF = 120° = angle EDF.
Then AB = ED = BF = BC + CF and since CF = CD, then AB = BC + CD.
If you have any questions as to why anything is true, you can ask
me in your thank-you note and I'll answer.