m∠MON = 130°
Solution:
Given m∠LON is a straight angle
m∠LOM = 4x + 30°, m∠MON = 8x + 90°
⇒ m∠LON = 180°
⇒ m∠LOM + m∠MON = 180°
⇒ 4x + 30° + 8x + 90° = 180°
Combine like terms together.
⇒ 4x + 8x + 30° + 90° = 180°
⇒ 12x + 120° = 180°
Subtract 120° on both sides of the equation.
⇒ 12x + 120° – 120° = 180° – 120°
⇒ 12x = 60°
Divide by 5 on both sides of the equation.
⇒ x = 5°
Substitute x = 5° in m∠MON.
⇒ m∠MON = 8x + 90°
= 8(5°) + 90°
= 40° + 90°
= 130°
Hence m∠MON = 130°.
