Answer:
None of the choices are correct.
Step-by-step explanation:
The angles are marked to show they are equal, therefore the line segment that divides the angle into two equal parts is an angle bisector.
Angle Bisector Theorem
The angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.
[tex]\implies \sf \dfrac{5}{4}=\dfrac{x}{12-x}[/tex]
[tex]\implies \sf5(12-x)=4x[/tex]
[tex]\implies \sf 60-5x=4x[/tex]
[tex]\implies \sf 9x=60[/tex]
[tex]\implies \sf x=\dfrac{60}{9}[/tex]
[tex]\sf \implies x=\dfrac{20}{3}[/tex]
