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Question
Is it possible to have a regular polygon whose interior angle is:
138°
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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RELATED QUESTIONS
Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
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