In the given rhombus, you have that the measure of angle EAB is
m∠EAB = 38⁰.
In order to determine the measure of angle EDC, you take into account that angle EAD and angle EAB together form a straight angle. Then, you have:
m∠EAB + m∠EAD = 180
m∠EAD = 180 - m∠EAB
m∠EAD = 180 - 38 = 142
Next, you consider that angle ADC is congruent to angle EAD:
m∠ADC = m∠EAD = 142
Finally, you take into account that angles ADC and EDC together form a straight angle:
m∠ADC + m∠EDC = 180
m∠EDC = 180 - m∠ADC
m∠EDC = 180 - 142 = 38
Hence, the measure of angle EDC is 38 degrees.