IMC 2011 Q9
9. In the diagram, \(XY\) is a straight line.
What is the value of \(x\)?
- A 170
- B 160
- C 150
- D 140
- E 130
Intermediate Mathematical Challenge 2011, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 170
In a triangle, an exterior angle is equal to the sum of the two interior, opposite angles. Repeatedly applying this theorem:
\(p = 150 - 80 = 70\);
\(q = p - 40 = 30\); \(r = q - 20 = 10\).
Therefore \(x = 180 - r = 170\).
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).