if each exterior angle of a regular polygon is 30degree . Find the no.of sides and sum of the interior angles of the polygon
if each exterior angle of a regular polygon is 30degree . Find the no.of sides and sum of the interior angles of the polygon
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Answer:
Step-by-step explanation:
Hey there !
Concept : Sum of Interior angle + Sum of Exterior angle = 180°
Let the interior angle be 'x'
=> Exterior angle = 3 * Interior angle = 3 x
=> x + 3x = 180°
=> 4x = 180°
=> x = 180 / 4
=> x = 45°
We also know that,
Exterior angle = 360° / n
Where n represents the number of sides of a polygon.
=> n = 360° / Exterior angle
=> n = 360° / 45°
=> n = 8
Hence it is a 8 sided polygon which is an octagon.
Hope my answer helped !