Copyright © University of Cambridge. All rights reserved.

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°. s 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.**View the archive of all weekly problems grouped by curriculum topic*

View the current weekly problem