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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Updated on: 10-Oct-2022

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