Question

Two alternate sides of a certain regular polygon meet at right angles when extended. Identify the polygon.

• A. Septagon
• B. Hexagon
• C. Octagon
• D. Nonagon

Answer 1

The correct option is C Octagon

From above figure, Each exterior angles = ${45}^{\circ }$

[In regular polygon all exterior angles are equal in measure]

Sum of all the exterior angles = ${360}^{\circ }$

$⟹n\times$ measure of one angle = ${360}^{\circ }$

[$n=$ number of sides of polygon]

$⟹n\times {45}^{\circ }={360}^{\circ }$

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

$⟹n=8$

Hence, the polygon is an Octagon.