Question
Is it possible to have a polygon whose each interior angle is $124^\circ?$
✓
Answer
Given each interior angle $=124^{\circ}$
So, each exterior angle $=180^{\circ}-124^{\circ}=56^{\circ}$
Thus, the number of sides of the polygon
$=\frac{360^{\circ}}{\text { Each exterior angle }}$
$=\frac{360^{\circ}}{56^{\circ}}$
$=6 \frac{3}{7} $
which is not a natural number
Therefore, no polygon is possible whose each interior angle is $124^{\circ}$.
So, each exterior angle $=180^{\circ}-124^{\circ}=56^{\circ}$
Thus, the number of sides of the polygon
$=\frac{360^{\circ}}{\text { Each exterior angle }}$
$=\frac{360^{\circ}}{56^{\circ}}$
$=6 \frac{3}{7} $
which is not a natural number
Therefore, no polygon is possible whose each interior angle is $124^{\circ}$.
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