If two supplementary angles differ by 74°, then one of the angles is:

Let us  consider that two supplementary angles are ∠A & ∠B.

Two angles are supplementary angle iff

∠A + ∠B = 180º   ----(1)

& two supplementary angles differ by 74°

∠A - ∠B = 74º     ---(2)

On adding equation  1 and 2 both ,

2∠A = 254º 

∠A = 127º 

by putting value of ∠A  in equation 1 ,

127º + ∠B = 180º

∠B = 53º

So, two angles are 127º and 53º.

Answer :- Option D :-  53º