Question

The sum of all the interior angles of a regular polygon is four times the sum of its exterior angles. The polygon is a

• A. hexagon
• B. triangle
• C. decagon
• D. nonagon

Answer 1

Answer: (C)

decagon

$\Rightarrow$ Let $n$ be the side of polygon.

$\Rightarrow$ Sum of interior angles = $(n-2)\times {180}^{\circ }$ ---- ( 1 )

According to the given question,

$\Rightarrow$ Sum of interior angles of polygon = 4(Sum of its exterior angles)

$\Rightarrow$ $(n-2)\times {180}^{\circ }=4\times {360}^{\circ }$ [From ( 1 )]

$\Rightarrow$ $(n-2)\times {180}^{\circ }={1440}^{\circ }$

$\Rightarrow$ $n-2=8$

$\therefore$ $n=10$

$\therefore$ The polygon is decagon.