Question
Find the number of sides in a regular polygon, when each interior angle is $: 120^\circ$
✓
Answer
Each interior angle of a regular polygon
$=\frac{( n -2) \times 180^{\circ}}{ n } $
$\Rightarrow \frac{( n -2)^{\circ} \times 180^{\circ}}{ n }=120^{\circ} $
$\Rightarrow 180^{\circ}( n -2)=120^{\circ}( n ) $
$\Rightarrow 3( n -2)=2 n $
$\Rightarrow n =6 .$
$=\frac{( n -2) \times 180^{\circ}}{ n } $
$\Rightarrow \frac{( n -2)^{\circ} \times 180^{\circ}}{ n }=120^{\circ} $
$\Rightarrow 180^{\circ}( n -2)=120^{\circ}( n ) $
$\Rightarrow 3( n -2)=2 n $
$\Rightarrow n =6 .$
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