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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