Answer:
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°
