Question

A regular polygon is inscribed in a circle. If a side subtends an angle of ${30}^{\circ }$ at the centre, what is the number of its sides?

• A. $10$
• B. $8$
• C. $6$
• D. $12$

Answer 1

The correct option is D $12$

For a polygon of 'n' sides, the angle subtended at the centre is $\frac{{360}^o}{n}$
Given, angle at the centre $={30}^o$
$=>\frac{{360}^o}{n}={30}^o$
$=>n=12$
Hence, the polygon has $12$ sides.