Question 15 Marks
The ratio between the interior angle and the exterior angle of a regular polygon is $2: 1.$ Find:
$(i)$ each exterior angle of the polygon ;
$(ii)$ number of sides in the polygon.
$(i)$ each exterior angle of the polygon ;
$(ii)$ number of sides in the polygon.
Answer
View full question & answer→Interior angle : exterior angle = 2 : 1
Let interior angle = 2x^\circ exterior angle = x^\circ
$\therefore 2x^\circ + x^\circ = 180^\circ$
$3x = 180^\circ$
$x = 60^\circ$
$\therefore$ Each exterior angle $= 60^\circ$
Let no.of. sides $= n$
$\frac{360^{\circ}}{n}=60^{\circ}$
$n=\frac{360^{\circ}}{60^{\circ}}$
$n = 6$
$\therefore (i) x = 60^\circ\ \ (ii) 6$
Let interior angle = 2x^\circ exterior angle = x^\circ
$\therefore 2x^\circ + x^\circ = 180^\circ$
$3x = 180^\circ$
$x = 60^\circ$
$\therefore$ Each exterior angle $= 60^\circ$
Let no.of. sides $= n$
$\frac{360^{\circ}}{n}=60^{\circ}$
$n=\frac{360^{\circ}}{60^{\circ}}$
$n = 6$
$\therefore (i) x = 60^\circ\ \ (ii) 6$