Question

Each exterior angel of a regular polygon is 20degree. how many sides are there in the polygon?what is the measure of each interior angel of the regular polygon?​​

Answer 1

Answer:

Let the number of sides of a regular polygon are n, its each exterior angle = 360°/n.

Accordingly :-

360°/n = 20°. => n = 360°/20° = 18 sides.

We know that:-

each interior angle + each exterior angle = 180°

each interior angle + 20° = 180°.

or, each interior angle =180° -20° = 160°.

Sum of all interior angles= 18×160° = 2880°.

Sum of all exterior angles = 18×20° = 360°

Sum of all the interior angles and all exterior angles= 2880°+360°= 3240.

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