IMC 2017 Q10
10. The diagram shows three rectangles.
What is the value of \(x\)?
- A 108
- B 104
- C 100
- D 96
- E 92
Intermediate Mathematical Challenge 2017, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 108
As shown in the diagram, the perpendicular from \(A\) to \(BC\) meets \(BC\) at \(D\). Because \(AD\) is parallel to two sides of the lower rectangle, \(\angle BAD = 43\)° and \(\angle DAC = 29\)° (corresponding angles in both cases). The angles at point \(A\) sum to 360°, so \(43 + 29 + 90 + x + 90 = 360\) and hence \(x = 108\).
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).