Copyright © University of Cambridge. All rights reserved.
'Rhombus Diagonal' printed from https://nrich.maths.org/
Show menu
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.