GK 2020 Q17
17. Bella took a square piece of paper and folded two of its sides to lie along the diagonal, as shown, to obtain a quadrilateral. What is the largest size of an angle in that quadrilateral?
- A 112.5°
- B 120°
- C 125°
- D 135°
- E 150°
Grey Kangaroo 2020, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 112.5°
Since the quadrilateral is formed by folding the 45° angles above and below the diagonal of the square in half, the size of the small angle of the quadrilateral is \(2 \times \left(\tfrac{1}{2} \times 45°\right) = 45°\). One angle of the quadrilateral is 90° and the other two are equal from the construction. Therefore, since the sum of the angles in a quadrilateral is 360°, the size of the equal angles is (360 − 90 − 45)° ÷ 2 = 225° ÷ 2 = 112.5°.
Solution © UK Mathematics Trust, from the GK 2020 solutions.