Explanation:
always remember :
the sum of all angles in a triangle is always 180°.
so, in triangle EFD
180 = E + F + D = 37 + 105 + D
D = 38°
since we know that the combination (sum) of B and D is 90° (right angle),
B + D = 90
B + 38 = 90
B = 52°
and now we look at the triangle ABC and its angles to get A, which then in turn gets us I of the triangle A(BD)I.
180 = A + B + C = A + 52 + 83
A = 45°
and that means for A(BD)I
180 = A + (B + D) + I = 45 + 90 + I
I = 45°
FYI : that means that the total triangle is an isoceles triangle (both legs are equally long : AB = DI).