Question

Each interior angle of a regular polygon is 90 degrees greater than each exterior angle. how many sides are there in the polygon?

Answer 1

In a polygon ,sum of interior angle and exterior angle is equal to 180 °
i.e interior angle + exterior angle = 180 ° ......(I)
according to question ,
interior angle = 90° + exterior angle ...... (ii)
putting the value of equation (ii) in equation (I)
we have , 90° + exterior angle + exterior angle = 180°
2* exterior angle = 180° - 90° =90°
exterior angle = 90°/2 = 45 °
Now , Number of sides of regular polygon = 360° / exterior angle
so , No. of sides = 360°/ 45° = 8

Answer 2

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