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Zielflug [23.3K]
4 years ago
14

Math: Angles and degrees

Mathematics
1 answer:
UkoKoshka [18]4 years ago
3 0

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°.

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