GK 2018 Q12
12. Valeriu draws a zig-zag line inside a rectangle, creating angles of 10°, 14°, 33° and 26° as shown.
What is the size of the angle marked \(\theta\)?
- A 11°
- B 12°
- C 16°
- D 17°
- E 33°
Grey Kangaroo 2018, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 11°
Add to the diagram three lines parallel to two of the sides of the rectangle, creating angles \(a\), \(b\), \(c\), \(d\), \(e\) and \(f\) as shown.
Since alternate angles formed by parallel lines are equal, we have \(a = 26°\) and \(f = 10°\). Since \(a + b = 33°\) and \(e + f = 14°\), we have \(b = 7°\) and \(e = 4°\). Similarly, since alternate angles are equal, we have \(c = b = 7°\) and \(d = e = 4°\). Therefore \(\theta = c + d = 7° + 4° = 11°\).
Solution © UK Mathematics Trust, from the GK 2018 solutions.