Question

$AB$, $BC$ and $CD$ are the three consecutive sides of a regular polygon. If $\angle BAC={15}^{\circ }$, find number of sides of the polygon.

• A. $12$
• B. $14$
• C. $15$
• D. $18$

Answer 1

The correct option is A $12$

AB, BC and CD are three consecutive sides of a regular polygon and $\angle BAC={15}^o$,

In $△BAC,AB=BC,$
Therefore, $\angle BCA=\angle BAC={15}^o$ ...(Isosceles Triangle)

Now,
$\angle BCA+\angle BAC+\angle ABC={180}^o$

${15}^o+{15}^o+\angle ABC={180}^o$
$\angle ABC={150}^o$
Each interior angle = ${150}^o$

Each interior angle of any regular polygon = $\frac{{180}^o(n-2)}{n}$

$\frac{{180}^o(n-2)}{n}={150}^o$
$=>{180}^{o}n-{150}^{o}n={360}^o$
$=>{30}^{o}n={360}^o$
$=>n=12$
Number of sides of polygon $=12$