PK 2016 Q16
16. The picture shows a cube with four marked angles, \(\angle WXY\), \(\angle XYZ\), \(\angle YZW\) and \(\angle ZWX\). What is the sum of these angles?
- A 315°
- B 330°
- C 345°
- D 360°
- E 375°
Pink Kangaroo 2016, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 330°
The lengths of \(WX\), \(XZ\) and \(ZW\) are all equal (each being the diagonal of a square face), hence triangle \(WXZ\) is equilateral and angle \(ZWX\) is 60°.
The other angles are all 90°, so the total of all four angles is \(90° + 90° + 90° + 60° = 330°\).
Solution © UK Mathematics Trust, from the PK 2016 solutions.