Answer
$m\angle A = 70^{\circ}$
$m\angle B = 110^{\circ}$
$m\angle C = 70^{\circ}$
$m\angle D = 110^{\circ}$
It is a parallelogram.
Work Step by Step
In a quadrilateral the sum of the interior angles equals to $360^{\circ}$.
So: $m\angle A + m\angle B+m\angle C + m\angle D =360^{\circ}$
$x+16+2\times (x+1) + \frac{3}{2} x-11 + \frac{7}{3} x -16 = 3x +\frac{3}{2} x + \frac{7}{3} x-9=\frac{41}{6} x -9=360^{\circ}$
$\frac{41}{6} x = 369^{\circ}$
$41x= 2214^{\circ}$
$x=54^{\circ}$
Then we calculate all the angles by substituting x by $54^{\circ}$
$m\angle A = 70^{\circ}$
$m\angle B = 110^{\circ}$
$m\angle C = 70^{\circ}$
$m\angle D = 110^{\circ}$
As the adjacent angles are supplementary, this quadrilateral is a parallelogram.
