Question

draw three different polygens and show that the sum of the exterior angles of any polygens is 360°​

Answer 1

Step-by-step explanation:

The sum of the exterior angles of a polygon having n sides.

We know that, exterior angle + interior adjacent angle = 180°

So, if the polygon has n sides, then

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

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

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

= n × 180° - n × 180° + 2 × 180°

= 180°n - 180°n + 360°

= 360°

Therefore, we conclude that sum of all exterior angles of the polygon having n sides = 360°