Question

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

• A. ${20}^{\circ }$
• B. ${30}^{\circ }$
• C. ${40}^{\circ }$
• D. none of the above

Answer 1

The correct option is C ${40}^{\circ }$

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 exterior angle = ${180}^o-{140}^o={40}^o$