Since STUV is a rhombus, ∠TUV and ∠SVU are supplementary.

Set the sum of their measures equal to 180° and plug in ∠SVU to solve for ∠TUV.

∠SVU+∠TUV=180°

128°+∠TUV=180° Plug in ∠SVU=128°

∠TUV=52° Subtract 128° from both sides

Also, SU bisects ∠TUV, so ∠SUV=∠SUT=12∠TUV. Next, plug in ∠TUV=52° to this equation and solve for ∠SUV.

∠SUV=12∠TUV

=12(52°) Plug in ∠TUV=52°

=26° Multiply

So, ∠SUV=26°.

Since GHIJ is a rhombus, opposite angles are congruent, GI bisects ∠HIJ, and HJ bisects ∠GJI.

So, ∠FJG≅∠FJI≅∠FHG≅∠FHI and ∠FGH≅∠FGJ≅∠FIH≅∠FIJ. Specifically ∠FHI=∠FJG=33°. Also, since GI and HJ are perpendicular, ∠HFI=90° and △FHI is a right triangle.

This means ∠FHI and ∠FIH are complementary. Set the sum of their measures equal to 90° and plug in ∠FHI=33° to solve for ∠FIH.

∠FHI+∠FIH=90°

33°+∠FIH=90° Plug in ∠FHI=33°

∠FIH=57° Subtract 33° from both sides

So, ∠FIH=57°.

Since GHIJ is a rhombus, opposite angles are congruent, GI bisects ∠HIJ, and HJ bisects ∠GJI

So, ∠FIH≅∠FIJ≅∠FGH≅∠FGJ and ∠FHG≅∠FHI≅∠FJG≅∠FJI. Specifically ∠FGJ=∠FIH=32°. Also, since GI and HJ are perpendicular, ∠GFJ=90° and △FGJ is a right triangle.