GK 2016 Q1
1. The triangle in the diagram contains a right angle.
What is the sum of the other two marked angles on the diagram?
- A 150°
- B 180°
- C 270°
- D 320°
- E 360°
Grey Kangaroo 2016, Question 1. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 270°
Since angles in a triangle add to 180° and one angle is given as 90°, the two blank angles in the triangle add to 90°. Since angles on a straight line add to 180°, the sum of the two marked angles and the two blank angles in the triangle is 2 × 180° = 360°. Therefore the sum of the two marked angles is 360° − 90° = 270°.
Solution © UK Mathematics Trust, from the GK 2016 solutions.