Question
Two alternate sides of a regular polygon, when produced, meet at the right angle.Find:$(i)$ The value of each exterior angle of the polygon$;(ii)$ The number of sides in the polygon.
✓
Answer
$(i)$ Let the measure of each exterior angle is $x$ and the number of sides is $n$.
Therefore we can write$:$
$n =\frac{360^{\circ}}{x}$
Now We have
$x+x+90^{\circ}=180^{\circ}$
$ 2 x=90^{\circ}$
$ x=45^{\circ}$
$(ii)$ Thus the number of sides in the polygon is $:$
$n =\frac{360^{\circ}}{45^{\circ}}$
$ n =8 .$
Therefore we can write$:$
$n =\frac{360^{\circ}}{x}$
Now We have
$x+x+90^{\circ}=180^{\circ}$
$ 2 x=90^{\circ}$
$ x=45^{\circ}$
$(ii)$ Thus the number of sides in the polygon is $:$
$n =\frac{360^{\circ}}{45^{\circ}}$
$ n =8 .$
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