Question

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

Answer 1

It has been stated in the Theorem 1 that if the sides of a quadrilateral are produced in order the sum of four exterior angles so formed is 360°.

This theorem is also known as Exterior Angle Sum Property.

Answer 2

Required solution :-

We know that,

Exterior angle + Interior adjacent angle = 180° [Linear pair]

Relation for polygon having n sides,

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

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

We know that,

Sum of interior angles is = (n-2) × 180

According to the question,

= n × 180 - (n-2) × 180

By transposing,

= n × 180 - n × 180 + 2 × 180

= 180n - 180n + 360

= 0 + 360

= 360°

Therefore, the sum of four exterior angles is 360°.