Question : The sum of all internal angles of a regular polygon whose one external angle is $20^\circ$ is:
Option 1: $6400^\circ$
Option 2: $3200^\circ$
Option 3: $2880^\circ$
Option 4: $1440^\circ$
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Correct Answer: $2880^\circ$
Solution : The number of sides $(n)$ in a regular polygon, $⇒n = \frac{360^\circ}{E}$ where $E$ is the external angle. Substituting $E = 20^\circ$ into the equation. $⇒n = \frac{360^\circ}{20^\circ} = 18$ The polygon has 18 sides. The sum $(S)$ of all internal angles of a polygon, $\therefore S = (n-2)× 180^\circ= (18-2) ×180^\circ = 16 ×180^\circ = 2880^\circ$ Hence, the correct answer is $2880^\circ$.
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Question : In a regular polygon if one of its internal angles is greater than the external angle by $132^\circ$, then the number of sides of the polygon is:
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