Question

$AB,BC$ and $CD$ are three consecutive sides of a regular polygon. If angle $BAC={20}^o$, find
(i) its each interior angle
(ii) its each exterior angle
(iii) the number of sides in the polygon

Answer 1

$\because \angle BAC={20}^{\circ }$

$⟹\angle BCA={20}^{\circ }$ and $\angle ABC={140}^{\circ }$ (Angle sum property)

(i) Each interior angle $={140}^{\circ }$

(ii) Each exterior angle $={180}^{\circ }-{140}^{\circ }={40}^{\circ }$

(iii) Number of sides of a regular polygon $n=\frac{{360}^{\circ }}{{40}^{\circ }}=9sides$

$\because$ Each exterior angle $=\frac{{360}^{\circ }}{n}$