Question

What is the measure of abd

Answer 1

Without figure its not possible. What does this D come from? is it a triangle or quadrilateral or exterior angle? Furnish this information then only it can be solved. 
I guess, it is sum of 2 angles. If that is right, 2x + 5x = 91 or 7x =91 or x =13 so 2x = 26. Does that work? 
Second is same type I guess! 
2x-1 + 5x +2 = 57. So 7x = 56, x = 8. So DBC = 42. 

Answer 2

BEC is 90 degrees.  EBC is 53 degrees. 

A triangle has 180 degrees.

ECB = 180 - 90 - 53 = 180 - 143 = 37 degrees
37 degrees is also equal to ECB since EAB = ECB.
AEB is 90 degrees because a line is 180 degrees and BEC is 90 degrees, and 180-90 = 90.

Once again, a triangle is 180 degrees, so:
 ABD = 180 - 90 - 37  
ABD = 180 - 127
ABD = 53 degrees