Question

Two alternate sides of a regular polygon, when produced, meet at the right angle. What is the number of sides in the polygon?

• A. 6
• B. 8
• C. 10
• D. 20

Answer 1

The correct option is B. $8$

Let the number of sides of regular polygon $=n$

$AB$ and $DC$ when produced at $P$ such that

$\angle P={90}^{\circ }$

$\because Interioranglesareequal,$

$\therefore \angle ABC=\angle BCD$

$\therefore {180}^{\circ }-\angle ABC={180}^{\circ }-\angle BCD$

$\therefore \angle PBC=\angle BCP$

$Given\angle P={90}^{\circ }$

$\therefore \angle PBC+\angle BCP={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

$\therefore \angle PBC=\angle BCP=\frac{1}{2}\times {90}^{\circ }={45}^{\circ }$

Each exterior angle $={45}^{\circ }$

$\Rightarrow {45}^{\circ }=\frac{{360}^{\circ }}{n}$

$\Rightarrow n=\frac{{360}^{\circ }}{{45}^{\circ }}$

$\Rightarrow n=8$

Hence, the number of sides os the polygon is $8$.