In the figure below, abd measures 32. what is the measure of abc?

The answer would be 64

To further explain, all triangles angles add up to 180 degrees. For triangle ABD, you have two angles measures already which add up to 122 degrees. 180 - 122 = 58 degrees. Since sides CD and DA are congruent that means angles CDB and ADB congruent as well. Therefore these angles equal 58 degrees each, and if you use common sense the measure of angle ABC would be 64 degrees because 32 + 32 = 64

Hope this helps!