Question

The ratio of exterior angle to interior angle of a regular polygon is $1:14$ respectively. Find the number of sides of the polygon

Answer 1

Ratio of exterior angle to interior angle is $1:14$

Let the angles be $x,14x$

Sum of $2$ angles $={180}^{\circ }$ ($\because$ they form a straight line )

$x+14x={180}^{\circ }\Rightarrow 15x={180}^{\circ }\Rightarrow x={12}^{\circ }$

$\therefore$ Each exterior angle is ${12}^{\circ }$

Sum of exterior angles$={360}^{\circ }$

No. of sides$=\frac{{360}^{\circ }}{{12}^{\circ }}=30$