In equilateral triangle DGH, every angle is 60&deg;, so angle GDH = 60&deg;.<br>In rhombus DEFG, diagonal DF bisects angle EDG, producing angle FDG = 30&deg;.<br>Angle FDH = angle FDG + angle GDH = 30&deg; + 60&deg; = 90&deg;.<br><br>Final Answer: 90&deg;