Is it possible to have a regular polygon whose interior angle is:… - Vidyadip

Question

Is it possible to have a regular polygon whose interior angle is: 155°

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Answer

No. of. sides = n
Each interior angle = 155°
$\therefore \frac{(2 n -4) \times 90^{\circ}}{ n }=155^{\circ}$
180n - 360° = 155n
180n - 155n = 360°
25n = 360°
$n =\frac{360^{\circ}}{25^{\circ}}$
$n =\frac{72^{\circ}}{5}$
$n =\frac{360^{\circ}}{25^{\circ}}$
$n =\frac{72^{\circ}}{5}$

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