PK 2017 Q22
22. Liza found the total of the interior angles of a convex polygon. She missed one of the angles and obtained the result 2017°. Which of the following was the angle she missed?
- A 37°
- B 53°
- C 97°
- D 127°
- E 143°
Pink Kangaroo 2017, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 143°
Let \(x°\) be the missing angle. The correct total of the angles is then \((2017 + x)°\). The interior sum of angles in a polygon with \(n\) sides is \(180(n - 2)°\), so we require \(2017 + x\) to be a multiple of 180. The larger multiples of 180 are 2160 plus any multiple of 180. Hence \(x = 143\) plus any multiple of 180. However, the polygon is convex so \(x = 143\).
Solution © UK Mathematics Trust, from the PK 2017 solutions.