ANSWER
x = 9
EXPLANATION
The sum of the interior angles of any triangle is 180º. In a right triangle, the sum of the angles that are not the right angle is 90º.
This is a right triangle, therefore:
[tex](4x-5)º+(7x+4)º=90º[/tex]To solve for x first we have to add like terms:
[tex]\begin{gathered} (4x+7x)-(5+4)=90 \\ 11x-9=90 \end{gathered}[/tex]Then we have to add 9 on both sides of the equation:
[tex]\begin{gathered} 11x-9+9=90+9 \\ 11x=99 \end{gathered}[/tex]And finally divide both sides by 11:
[tex]\begin{gathered} \frac{11x}{11}=\frac{99}{11} \\ x=9 \end{gathered}[/tex]