IMC 2004 Q4
4. What is the value of \(a + b + c + d + e + f\)?
- A 360
- B 540
- C 720
- D 900
- E it depends on the triangle
Intermediate Mathematical Challenge 2004, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 720
The angles marked \(a\)°, \(c\)° and \(e\)° may be considered to be the exterior angles of the triangle and therefore have a total of 360°. As \(b\)° = \(a\)°, \(d\)° = \(c\)° and \(f\)° = \(e\)° (all pairs of vertically opposite angles), \(b + d + f = 360\). So \(a + b + c + d + e + f = 720\).
Solution © UK Mathematics Trust, from the IMC 2004 solutions.