IMC 2009 Q12
12. The diagram shows a square inside a regular hexagon. What is the size of the marked angle at \(X\)?
- A 45°
- B 50°
- C 60°
- D 75°
- E 80°
Intermediate Mathematical Challenge 2009, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 75°
Let \(Y\) and \(Z\) be the points shown. The interior angle of a regular hexagon is 120°, so \(\angle XZY\) = 120° − 90° = 30°. The side of the square has the same length as the side of the regular hexagon, so \(YZ = XZ\). Hence triangle \(XYZ\) is isosceles and \(\angle ZXY = \angle ZYX = \tfrac{1}{2}\)(180° − 30°) = 75°.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.