The measure of the smallest angle of the quadrilateral is 60° .
In the question ,
it is given that ,
the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .
So , the measure of the largest angle is = 9x
and the measure of the smallest angle is = 4x .
we know that the sum of the measure of all the angles of the quadrilateral is 360° .
that means ,
4x + 5x + 6x + 9x = 360°
24x = 360
dividing both sides by 24 ,
x = 360/24
x = 15 .
the smallest angle is = 4(15) = 60°
Therefore , The measure of the smallest angle of the quadrilateral is 60° .
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