Question

In a regular polygon, the exterior and interior angles are in the ration $1:4$. The number of sides of the polygon is

• A. $10$
• B. $12$
• C. $15$
• D. $16$

Answer 1

Answer: (A)

$10$

Let the exterior angle be x, then interior angle will be $4x$
We know that,
Interior angle + Exterior angle = ${180}^0$
$\therefore x+4x={180}^0$
$x=\frac{180}{5}={36}^0$
Interior angle = $4x=4\times {36}^0={144}^0$
We know that,
Interior angle of a polygon $=\frac{(n-2)}{n}\times {180}^0$
${144}^0=\frac{(n-2)}{n}\times {180}^0$
${144}^{0}n={180}^{0}n-{360}^0$
${180}^{0}n-{144}^{0}n={360}^0$
${36}^{0}n={360}^0$
$\therefore n=10$
So, number or sides = $10$