Answer
$27^{\circ}$
Work Step by Step
Consider a triangle $\text{DEF}$.
Apply the Law of Sines.
$\dfrac{\sin D}{d} =\dfrac{\sin E}{e} =\dfrac{\sin F}{f} $
Rearrange the above two ratio setup to obtain:
$\dfrac{\sin D}{d} =\dfrac{\sin F}{f}\\\dfrac{\sin D}{16} =\dfrac{\sin 43^{\circ}}{ 24} \\ \sin D=\dfrac{16 \sin 43^{\circ}}{24} $
In order to calculate $\angle{D}$, we need to rearrange the equation (1) as follows:
$\angle{D} =\sin^{-1} (\dfrac{16 \sin 43^{\circ}}{24}) \approx 27^{\circ}$
