Question

AB, BC and CD are three consecutive sides of a regular polygon. If $\angle BAC=$${20}^{\circ }$, Find the number of sides in the polygon

• A. $8$
• B. $7$
• C. $9$
• D. $10$

Answer 1

The correct option is C $9$

AB, BC and CD are three consecutive sides of a regular polygon and $\angle BAC={20}^o$,
In $△BAC,AB=BC,$
Therefore, $\angle BCA=\angle BAC={20}^o$ (Isosceles Triangle)
Now,
$\angle BCA+\angle BAC+\angle ABC={180}^o$
${20}^o+{20}^o+\angle ABC={180}^o$
$\angle ABC={140}^o$
Each interior angle = ${140}^o$
Each interior angle of any regular polygon = $\frac{{180}^o(n-2)}{n}$
$\frac{{180}^o(n-2)}{n}={140}^o$
$=>{180}^{o}n-{140}^{o}n={360}^o$
$=>{40}^{o}n={360}^o$
$=>n=9$
Number of sides of polygon $=9$