If the three interior angles of a quadrilateral are $86°, 120°, and 40°$, then find the measure of the fourth interior angle.

We know that, the sum of the interior angles of an irregular polygon = $(n-2)\times {180}^o$, where 'n' is the number of sides. 

Since it is a quadrilateral, therefore, n = 4.

Hence, the sum of the interior angles of the quadrilateral $=(n-2)\times {180}^o=(4-2)\times {180}^o={360}^o$ 

Let the fourth interior angle be x. 

Therefore,

$\begin{array}{r}{86}^{\circ }+{120}^{\circ }+{40}^{\circ }+x={360}^{\circ }\\ {246}^{\circ }+x={360}^{\circ }\\ x={360}^{\circ }-{246}^{\circ }\\ x={114}^{\circ }\end{array}$ 

Therefore, the fourth interior angle is $114°$.