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?
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
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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 °.