Rhombus Diagonal
Weekly Problem 19 - 2014
The diagram shows a rhombus and an isosceles triangle. Can you work out the size of the angle JFI?
The diagram shows a rhombus and an isosceles triangle. Can you work out the size of the angle JFI?
Age
11 to 14
Challenge level
Problem
Image
The diagram on the right shows a rhombus FGHI and an isosceles triangle FGJ in which GF = GJ. Angle FJI = 111 °.
What is the size of angle JFI?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Image
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 °.