IMC 2014 Q3
3. An equilateral triangle is placed inside a larger equilateral triangle so that the diagram has three lines of symmetry.
What is the value of \(x\)?
- A 100
- B 110
- C 120
- D 130
- E 150
Intermediate Mathematical Challenge 2014, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 150
Clearly \(AD\) lies along one of the lines of symmetry of the figure. So \(\angle FDA = \angle EDA = x^\circ\). Triangle \(DEF\) is equilateral so \(\angle EDF = 60^\circ\).
The angles which meet at a point sum to 360°, so \(x + x + 60 = 360\).
Therefore \(x = 150\).
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).