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to facilitate the exercise we will draw the triangle
We start using the area
[tex]A=\frac{b\times h}{2}[/tex]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)
[tex]\begin{gathered} 2312=\frac{96\times h}{2} \\ \\ h=\frac{2312\times2}{96} \\ \\ h=\frac{289}{6} \end{gathered}[/tex]now to calculate the measure of the angles we can solve the red triangle
first we find Y using trigonometric ratio of the sine
[tex]\sin (\alpha)=\frac{O}{H}[/tex]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
[tex]\sin (y)=\frac{\frac{289}{6}}{93}[/tex]simplify
[tex]\sin (y)=\frac{289}{558}[/tex]and solve for y
[tex]\begin{gathered} y=\sin ^{-1}(\frac{289}{558}) \\ \\ y=31.2 \end{gathered}[/tex]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°
[tex]\begin{gathered} y+x=180 \\ 31.2+x=180 \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=180-31.2 \\ x=148.8 \end{gathered}[/tex]measure of the included angle is 148.8°
