Question

the interior angle of n sided regular polygon is 48° more than the interior angle of regular hexagon .Find n
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Answer 1

Answer:

No such polygon exists.

Step-by-step explanation:

As we know sum of all interior angle of a hexagon is equal to 720° and one single angle is = 720° / 6 = 120°

The value of the interior angle of n sided regular polygon is = 120° + 48° = 168°

The value of n is equal to 168n / (n -2)*180 = 0 => 168n / 180n - 360 = 0

=> 84n / 90n - 360 = 0

=> 42n / 45n - 360 = 0

=> 42n / 45n = 360

Hence, no such polygon exists.

Answer 2

Interior angle of hexagon=4*180/6=120

hence, the internal angle of n sided polygon=168

hence, its exterior angle=180-168=12

we know that sum of all the exterior angles of an n-sided polygon taken anti-clockwise/clockwise=360

Therefore, n=360/12=30

Hope this helps...I guess you found this question in the Olympiad Mathematics book...