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Question
Is it possible to have a polygon whose each interior angle is 105°?
Solution
Given each interior angle = 105°
So, each exterior angle = 180° - 105° = 75°
Thus, the number of sides of the polygon
= `(360°)/"Each exterior angle"`
= `(360°)/(75°)`
= `4(4)/(5)`
which is not a natural number
Therefore, no polygon is possible whose each interior angle is 105°.
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