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Rhombus Diagonal

Age 11 to 14 Short
Challenge Level


Adjacent angles on a straight line add up to 180 °, so ∠GJF = 180 ° -111 ° = 69 °.
In triangle FGJ, GJ = GF so âˆ GFJ = âˆ GJF. Therefore âˆ FGJ =(180 - 2 x 69) ° = 42 °.  Since FGHI is a rhombus, FG = FI and therefore âˆ GIF = âˆ FGI = 42 °.

Finally, from triangle FJI, âˆ 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.