IMC 2007 Q10
10. The diagram shows three squares drawn on the sides of a triangle.
What is the sum of the three marked angles?
- A 180°
- B 270°
- C 360°
- D 450°
- E It depends on the shape of the triangle
Intermediate Mathematical Challenge 2007, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 360°
At each vertex of the triangle, four angles meet. In all, these twelve angles comprise six right angles, the three interior angles of the triangle and the three marked angles. So the sum of the marked angles = 3 × 360° − 6 × 90° − 180° = 360°.
Solution © UK Mathematics Trust, from the IMC 2007 solutions.