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the sides of a polygon is in ratio 4 : 5 : 11 : 12 : 13 .find the exterior
Given: the sides of a polygon is in ratio 4 : 5 : 11 : 12 : 13
To find: The exterior angles
Solution:
Let the angles be $x$
Therefore, $4x:5x:11x:12x:13x$
There are 5 sides hence its a pentagon
Sum of interior angle of pentagon
=$(x-2) \times180$
=$(5-2)\times 180$
=$3\times180$
=540
=>$4x+5x=11x+12x+13x$
=>$45x=540$
=>$x= \frac{540}{45}$
So, measure of each exterior angles are
$4x = 4\times12 =48$
$5x = 5\times12 =60$
$11x = 11\times12 =133$
$12x = 12\times12 =144$
$13x = 13\times12 =156$
So, the exterior angles are
$180-48=132$
$180-60=120$
$180-133=48$
$180-144=36$
$180-156=24$
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