Question

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

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$

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 = ${45}^o$