IMC 2009 Q4
4. The diagram shows two isosceles triangles, in which the four angles marked \(x\)° are equal. The two angles marked \(y\)° are also equal. Which of the following is always true?
- A \(y = 2x\)
- B \(y = x + 30\)
- C \(y = x + 60\)
- D \(y = x + 90\)
- E \(y = 180 - x\)
Intermediate Mathematical Challenge 2009, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A \(y = 2x\)
The two acute angles in the quadrilateral in the centre of the diagram are both \((180 - 2x)\)° and the two obtuse angles are both \(y\)°, so \(360 - 4x + 2y = 360\). So \(y = 2x\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.