IMC 2005 Q13
13. The diagram shows two equilateral triangles.
What is the value of \(x\)?
- A 70
- B 60
- C 50
- D 40
- E 30
Intermediate Mathematical Challenge 2005, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 40
Considering the angles at \(B\) and \(E\):
\(\angle CBE\) = (180 − 75 − 60)° = 45°;
\(\angle DEB\) = (180 − 65 − 60)° = 55°. Therefore
\(\angle GHB\) = (45 + 55)° = 100° (exterior angle theorem) and, using the same theorem, \(\angle HGC\) = (100 − 60)° = 40°.
Solution © UK Mathematics Trust, from the IMC 2005 solutions.