IMC 2017 Q6
6. The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6.
What is the difference between the largest angle and the smallest angle?
- A 30°
- B 40°
- C 50°
- D 60°
- E 70°
Intermediate Mathematical Challenge 2017, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 60°
The sum of the interior angles of a quadrilateral is 360°. So the smallest angle in the quadrilateral is \(3 \times \frac{360°}{3 + 4 + 5 + 6} = 60\)° and the largest angle is \(6 \times \frac{360°}{3 + 4 + 5 + 6} = 120\)°.
Hence the required difference is 60°.
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).