Question

If any interior angle of a regular polygon exceeds the exterior angle by 100, then the number of sides of the polygon is

• A. 7
• B. 8
• C. 9
• D. 6

Answer 1

The correct option is C 9

Let there be n sides, then sum of interior angles $=(n-2)180$

Each interior angle will be $=\frac{n-2}{n}\left(180\right)$

Each exterior angle will be $=180-\left(\frac{n-2}{n}\right)\times 180$

Thus,

$\frac{n-2}{n}\left(180\right)$$-$ $(180-$$\left(\frac{n-2}{n}\right)\times 180$) = 100

$\frac{n-2}{n}\left(2\right)\left(180\right)=280$

$\Rightarrow 9n-18=7n$

$\Rightarrow n=9$