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Question
Is it possible to have a regular polygon whose interior angle is: 155°
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Solution
No. of. sides = n
Each interior angle = 155°
∴ `(("2n" - 4) xx 90^circ)/"n" = 155^circ`
180n - 360° = 155n
180n - 155n = 360°
25n = 360°
n = `(360°)/(25°)`
n = `72^circ/5`
Which is not a whole number.
Hence, it is not possible to have a regular polygon whose interior angle is 155°.
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