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Question
Is it possible to have a regular polygon whose interior angle is:
138°
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Solution
Let no. of sides = n
each interior angle = 138°
`therefore ("n" - 2)/"n" xx 180^circ = 138^circ`
180n - 360° = 138n
180n - 138n = 360°
42n = 360°
n = `(360°)/42`
n = `60^circ/7`
which is not a whole number.
Hence it is not possible to have a regular polygon whose interior angle is 138°.
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