IMC 2016 Q7
7. In the diagram, what is the value of \(x\)?
- A 23
- B 24
- C 25
- D 26
- E 27
Intermediate Mathematical Challenge 2016, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 25
The angles at a point sum to 360° so
\(75 + z = 360\) and \(y + x = 360\).
Therefore \(75 + z + y + x = 720\).
The sum of the interior angles of a hexagon is 4 × 180° = 720°.
Therefore
\(27 + 24 + y + 23 + 26 + z = 720\), so \(75 + z + y + x = 27 + 24 + y + 23 + 26 + z\).
Hence \(75 + x = 27 + 24 + 23 + 26 = 100\). So \(x = 100 - 75 = 25\).
Solution © UK Mathematics Trust, from the IMC 2016 solutions. Longer versions with investigations: Solutions and investigations (PDF).