Angle LON is a straight angle
Angle MON= 3x+89
Angle LOM=8x+58
Find Angle MON:

Angle MON is 98°

Step-by-step explanation:

The measure of the straight angle is 180°

∵ ∠LON is a straight angle

∴ m∠LON = 180°

∵ Ray OM intersects line LN at O

∴ OM divides ∠LON into two angles ∠LOM and ∠MON

∴ m∠LOM + m∠MON = m∠LON

- Substitute m∠LON by 180°

∴ m∠LOM + m∠MON = 180°

∵ m∠LOM = 8 x + 58

∵ m∠MON = 3 x + 89

- Substitute them in the equation above

∴ (8x + 58) + (3 x + 89) = 180°

- Add the like terms in the left hand side

∴ (8 x + 3 x) + (58 + 89) = 180°

∴ 11 x + 147 = 180

- Subtract 147 from both sides

∴ 11 x = 33

- Divide both sides by 11

∴ x = 3

Substitute the value of x in the measure of angle MON to find it

∵ m∠MON = 3(3) + 89

∴ m∠MON = 9 + 89

∴ m∠MON = 98°