Question

Two alternates sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (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 $=8$