How many sides does a regular polygon have has,each angle of which measure 16°?
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Answer:1) Let the polygon be n-sided.
Given that Each interior angle measures 156°
So, ( n-2 ) × 180 / n = 156
=> 180n - 360 = 156n .
=> 180n - 156n = 360
=> 24 n = 360
=> n = 360/24 = 180/12 = 90/6 = 15 .
=> n = 15 sides.
Therefore ,The polygon with each interior angle 156° has 15 sides.
2) Let the polygon be n-sided.
Given that Each interior angle measures 108°
So, ( n-2 ) × 180 / n = 108°
=> 180n - 360 = 108n .
=> 180n - 108n = 360
=> 72 n = 360
=> n = 360/72= 5
=> n = 5 sides.
Therefore ,The polygon with each interior angle 108° has 5 sides.
Step-by-step explanation:
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