Notice that the given angles form a straight angle, therefore:
[tex](5x+4)^{\circ}+(x-2)^{\circ}+(3x+7)^{\circ}=180^{\circ}.[/tex]
Then:
[tex]5x+4+x-2+3x+7=180.[/tex]
Solving the above equation for x we get:
[tex]\begin{gathered} 9x+9=180, \\ 9x=180-9=171, \\ x=19. \end{gathered}[/tex]
Answer: The angles are:
[tex]\begin{gathered} (5\cdot19+4)^{\circ}=99^{\circ}, \\ (19-2)^{\circ}=17^{\circ}, \\ (3\cdot19+7)=64^{\circ}. \end{gathered}[/tex]
