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'Rhombus Diagonal' printed from https://nrich.maths.org/
Adjacent angles on a straight line add up to 180 °, so ∠GJF = 180 ° -111 ° = 69 °.
In triangle FGJ, GJ = GF so ∠GFJ = ∠GJF. Therefore ∠FGJ =(180 - 2 x 69) ° = 42 °. Since FGHI is a rhombus, FG = FI and therefore ∠GIF = ∠FGI = 42 °.
Finally, from triangle FJI, ∠JFI = (180 - 111 - 42) ° = 27 °.