If x is an acute angle and $\sin (x+28°)=\cos (3x-78°)$   then the angle  is

$\begin{array}{l}\sin (x+28°)=\cos (3x-78°)\\ \Rightarrow \sin (x+28)=\sin (90°+3x-78°)\\ \sin (x+28°)=\sin (3x+12°)\\ x+28°=12°+3x\\ \Rightarrow 2x=16°\\ \Rightarrow x=8°\end{array}$

(Or)

$\begin{array}{l}\sin (x+28°)=\sin (90°-3x+78°)\\ \sin (x+28°)=\sin (168°-3x)\\ x+28°=168°-3x\\ \Rightarrow 4x=140°\\ x=35°\end{array}$