Question

Math Help Help Fast Alot of points

Answer 1

Here mark the angles

• m<FHG=75
• m<FGH=55
• m<GHI=59°
• m<GIH=63°

By using angle sum property

• m<IGH=180-122=58

So

• m<FGH < m<IGH <m<GHI <m<GIH <m <FHG

So

• FH<IH<GI<GH<FG

Answer 2

IH < GI < GH < FH < FG

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