Answer:
∠MON = 98°
Explanation:
It is given that ∠LON is a straight line.
∠MON = 3x+89
and
∠LOM = 8x+58
If LON is a straight line. It means,
∠MON + ∠LOM = 180 (Linear pair)
Putting values,
3x+89 + 8x+58 = 180
11x + 147 = 180
11x = 180-147
11x = 33
x = 3
So, ∠MON = 3(3)+89
= 9+89
= 98
Hence, the value of ∠MON is equal to 98°.