Answer:
∠B = 142 .15'
Step-by-step explanation:
Given : If ∠A and ∠B are supplementary and  m∠A = 37°45',
To find :  m∠B = ______. 
Solution : We have given that ∠A and ∠B  are supplementary.
We know that sum of two supplementary angle is 180 degree.
Then  ∠A + ∠B = 180°
We have given  m∠A = 37°45',
Plugging the value of angle A
  37°45'+ ∠B = 180°
On subtracting by   37°45' both sides
 ∠B = 180° - 37°45' 
Now convert the 45' in to degree 
45' = 0.75 degree
Then 37° + 0.75° = 37.75° 
 ∠B = 180° - 37.75°
 ∠B = 142 .25 ° 
We need our answer in degree and mint
1°  = 60' 
0.25°  =15'
∠B = 142 .15'
Therefore, ∠B = 142 .15'