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is it possible to have a regular polygon in which the interior and exterior angles are in the ratio 3:2?

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Answer:

see explanation

Explanation:

the sum of an exterior angle + interior angle of a polygon = 180°

sum the parts of the ratio 3 : 2 , 3 + 2 = 5 parts

180° ÷ 5 = 36° ← value of 1 part of the ratio , then

3 parts = 3 × 36° = 108° ← interior angle

2 parts = 2 × 36° = 72° ← exterior angle

the sum of the exterior angles of a polygon = 360° , then


(360)/(72) = 5 ← number of sides

the sum of the interior angles of a polygon is calculated as

sum = 180° ( n - 2) ← n is the number of sides

if n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

and 5 × 108° = 540°

Thus a regular polygon with 5 sides ( Pentagon ) has

interior angle : exterior angle = 3 : 2

User Ronit Oommen
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