Question

An exterior angle of regular polygon is ${12}^{\circ }$ the sum of all the interior angles is

• A. ${4040}^{\circ }$
• B. ${5040}^{\circ }$
• C. ${6040}^{\circ }$
• D. ${7040}^{\circ }$

Answer 1

The correct option is B ${5040}^{\circ }$

Given the exterior angle of regular polygon is 12

We know each exterior angle of regular polygon=$\frac{360}{n}$ where n is the sides of polygon

$\frac{360}{n}=12\Rightarrow n=30$

we know that interior angle of regular polygon=$180(n-2)=180(30-2)={5040}^0$