Question

Two alternate sides of a regular polygon, when produced, meet at a right angle. Find the number of sides of the polygon.

• A. $3$
• B. $8$
• C. $2$
• D. $9$

Answer 1

The correct option is B $8$

In a regular polygon all the exterior angles have the same measure.

When two alternate sides of a polygon are extended a triangle.

If AB, BC and CD are the sides of a regular polygon and AB and CD when produced meet at P forming a right triangle.

Now, in $△CPB,\angle PCB=\angle PBC={45}^o$

Therefore, exterior angle of the polygon = ${45}^o$
Exterior angle of a regular polygon = $\frac{{360}^o}{n}$
$=>{45}^o=\frac{{360}^o}{n}$
$=>n=8$
Number of sides of the polygon = $8$