Question

If the ratio number of diagonal to
sides of a polygon is 7:1 . find The interior
angle sum ​

Answer 1

Answer:

Since, interior angle + exterior angle of any polygon ,at one vertex = 180° & the ratio of these angles = 7:2

=> 7x + 2x = 180

=> 9x = 180

=> x = 20

=> 7x = 140° & 2x = 40°

=> Here interior angle has to be 140° as interior angle of any regular polygon can not be less than 60°

Now, we know the formula of each interior angle of a regular polygon = (n-2)180 / n , (where n is the number of sides of the polygon)

=> (n-2)*180 / n = 140

=> 180n - 140n = 360

=> 40n = 360

=> n = 9

So, the regular polygon has 9 equal sides.

Answer 2

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