Question

Let $S$ be the sum of the interior angles of a polygon $P$ for which each interior angle is $7\frac{1}{2}$ times the exterior angle at the same vertex. Then

• A. $S={2660}^{\circ }$ and $P$ may be regular
• B. $S={2660}^{\circ }$ and $P$ is not regular
• C. $S={2700}^{\circ }$ and $P$ is regular
• D. $S={2700}^{\circ }$ and $P$ is not regular
• E. $S={2700}^{\circ }$ and $P$ may or may not be regular

Answer 1

The correct option is D $S={2700}^{\circ }$ and $P$ is not regular

Sum of interior angles $=7.5\ast$ sum of exterior angles

$S=7.5\ast {360}^{\circ }$

$S={2700}^{\circ }$

And the polygon is not a rectangle polygon.