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....
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Answer:
360 degrees
Step-by-step explanation:
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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