IMC 2010 Q2
2. Three of the interior angles of a given quadrilateral are each 80°. What is the fourth angle of this quadrilateral?
- A 120°
- B 110°
- C 100°
- D 90°
- E 80°
Intermediate Mathematical Challenge 2010, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 120°
The sum of the interior angles of a quadrilateral is 360°, so the fourth angle is (360 − 3 × 80)° = 120°.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.