Answer:
IH < GI < GH < FH < FG
Step-by-step explanation:
Find missing angles
Sum of interior angles of a triangle = 180°
⇒ ∠GFH = 180 - 55 - 75 = 50°
⇒ ∠IGH = 180 - 59 - 63 = 58°
Side lengths in relation to interior angles
The longest side of a triangle is opposite the largest interior angle, and the shortest side is opposite the smallest angle.
Therefore, angles/sides in order of least to greatest:
ΔIGH
∠IGH = 58 → its opposite side is IH
∠GHI = 59 → its opposite side is GI
∠G|H = 63 → its opposite side is GH
Therefore, IH < GI < GH
ΔFGH
∠GFH = 50 → its opposite side is GH
∠FGH = 55 → its opposite side is FH
∠FHG = 75 → its opposite side is FG
Therefore, GH < FH < FG
Combining: IH < GI < GH < FH < FG
