PK 2019 Q7
7. Two angles are marked on the 3 × 3 grid of squares.
Which of the following statements about the angles is correct?
- A \(\alpha = \beta\)
- B \(2\alpha + \beta = 90\)
- C \(\alpha + \beta = 60\)
- D \(2\beta + \alpha = 90\)
- E \(\alpha + \beta = 45\)
Pink Kangaroo 2019, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B \(2\alpha + \beta = 90\)
The triangle \(PQR\) is congruent to the triangle \(TQS\) since they are right-angled triangles with sides of length 3 and 2. Hence the angle \(PQR\) is also \(\alpha°\) and then \(\alpha + \beta + \alpha = 90\). One can check that the other statements are false.
Solution © UK Mathematics Trust, from the PK 2019 solutions.