Question

$AB$, $BC$ and $CD$ are the three consecutive sides of a regular polygon. If $\angle BAC={15}^{\circ }$, find each interior angle of the polygon (in degrees)

• A. ${150}^{\circ }$
• B. ${140}^{\circ }$
• C. ${135}^{\circ }$
• D. none of these

Answer 1

The correct option is A ${150}^{\circ }$

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 = ${150}^o$