Question

The measurement of each exterior angle of a regular polygon is ${40}^{\circ }$. How many sides does it have?

• A. $8$
• B. $9$
• C. $6$
• D. $10$

Answer 1

Answer: (B)

$\left(9\right)$

Given exterior angle $={40}^{\circ }$
But we know that the sum of all exterior angles of a polygon $={360}^{\circ }$

Let us assume that the polygon has $x$ sides, then
$\Rightarrow 40\times x={360}^{\circ }$
$x=\frac{360}{40}$
$\therefore x=9$
Hence, the polygon has $9$ sides.