Question

If the exterior angle of a regular polygon is one-fifth of the interior angle then find the value of the exterior angle.

• A. 30${}^{\circ }$
• B. 45${}^{\circ }$
• C. 90${}^{\circ }$
• D. 60${}^{\circ }$

Answer 1

The correct option is A

30${}^{\circ }$

Let the exterior angle of the given polygon be $x^{\circ }$

Given, the exterior angle is one-fifth of the interior angle

$\Rightarrow$ $\frac{1}{5}\times$ interior angle = $x$

$\Rightarrow$ interior angle = 5$x$

$\because$ an exterior angle + interior angle = 180${}^{\circ }$

$\Rightarrow$ 5$x$ + $x$ = 180${}^{\circ }$

$\Rightarrow$ 6$x$ = 180${}^{\circ }$

$\Rightarrow$ $x$ = 30${}^{\circ }$