IMC 2012 Q3
3. An equilateral triangle, a square and a pentagon all have the same side length. The triangle is drawn on and above the top edge of the square and the pentagon is drawn on and below the bottom edge of the square. What is the sum of the interior angles of the resulting polygon?
- A 10 × 180°
- B 9 × 180°
- C 8 × 180°
- D 7 × 180°
- E 6 × 180°
Intermediate Mathematical Challenge 2012, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 6 × 180°
The diagram shows that the interior angles of the polygon may be divided up to form the interior angles of six triangles. So their sum is 6 × 180°.
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).