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Rhombus Diagonal

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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°.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.