[tex]m \angle M O N=89^{\circ}[/tex]
Solution:
Given [tex]m \angle L O N[/tex] is a straight angle.
[tex]m \angle M O N=3 x+89^{\circ}[/tex]
[tex]m \angle L O M=8 x+58^{\circ}[/tex]
To find the value of [tex]m \angle M O N[/tex]:
Sum of the adjacent angles in a straight line = 180°
[tex]m \angle M O N+m \angle L O M=180^{\circ}[/tex]
[tex]\begin{aligned}&3 x+89^{\circ}+8 x+58^{\circ}=180^{\circ}\\&11 x+147^{\circ}=180^{\circ}\\&11 x=180^{\circ}-147^{\circ}\\&11 x=33^{\circ}\end{aligned}[/tex]
[tex]x=3^{\circ}[/tex]
Substitute x = 3° in [tex]$m \angle M O N$[/tex].
[tex]$m \angle M O N=3 (3^{\circ})+89^{\circ}$[/tex]
[tex]=9^{\circ}+89^{\circ}[/tex]
[tex]=98^{\circ}[/tex]
[tex]m \angle M O N=89^{\circ}[/tex]
Hence m∠MON = 89°.
