The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?

We know that, exterior angle + interior adjacent angle = 180° [Linear pair]

Applying relation for polygon having n sides

Sum of all exterior angles + Sum of all interior angles = n × 180°

Therfore sum of all exterior angles = n × 180° - Sum of all interior angles

Sum of all exterior angles = n × 180° - (n -2) × 180° [Sum of interior angles is = (n - 2) x 180°]

Sum of all exterior angles = n × 180° - n × 180° + 2 × 180°

Sum of all exterior angles = 180°n - 180°n + 360°

Sum of all exterior angles = 360°