to facilitate the exercise we will draw the triangle
We start using the area

where A is the area, b the base and h the height
if we replace A=2312 and b=96 we can calculate the height(h)

now to calculate the measure of the angles we can solve the red triangle
first we find Y using trigonometric ratio of the sine

where alpha is the reference angle, O the opposite side from the angle and H the hypotenuse of the triangle
using Y like reference angle and replacing

simplify

and solve for y

value of angle y is 31.2°
Y and X are complementary because make a right line then if we add both numbers the solution is 180°

and solve for x

measure of the included angle is 148.8°