IMC 2011 Q7
7. What is the value of \(x\) in this diagram?
- A 30
- B 35
- C 40
- D 45
- E 50
Intermediate Mathematical Challenge 2011, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 30
Alternate angles \(BDF\) and \(DFG\) are equal, so lines \(BD\) and \(FG\) are parallel. Therefore \(\angle BCA = \angle FGC = 80^\circ\) (corresponding angles).
Consider triangle \(ABC\): \(x + 70 + 80 = 180\), so \(x = 30\).
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).