Question

The ratio of interior angle to exterior angle regular polygon is 49:1 then the number of side​

Answer 1

Given : The ratio of interior angle to exterior angle regular polygon is 49:1

To Find : Number of sides

Solution:

Sum of interior angle + exterior angle = 180°  ( Linear Pair)

ratio of interior angle to exterior angle regular polygon is 49:1

Ley say exterior angle = x

Then Interior angle = 49x

=> 49x + x  = 180

=> 50x = 180

=> x = 180/50

=> x = 18/5

Interior angle = 49x  = 49(18/5)

Interior angle of regular polygon = (n-2)*180/n

 (n-2)*180/n  = 49(18/5)

=> (n-2)*50  = 49n

=> 50n - 100 = 49n

=>  n = 100

Number of sides = 100

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