Question

The sides of a quadrilateral are extended in order to form exterior angles.What is the sum of these exterior angles? Answer should be detailed for good explanation. Best answer would be marked brainliest with 47 points

Answer 1

Answer:

360 degrees

Step-by-step explanation:

the sum of any polygon (exterior angles) will be 360 degrees

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°  

Therefore, measure of each exterior angle of the regular polygon = 360°/n

Also, number of sides of the polygon = 360°/each exterior angle

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