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°.
Answer:
x = 7, y = 30 and x = 3, y = 10
Step-by-step explanation:
5x - y = 5, then y = 5x - 5
2y - x^2 = 11
2(5x - 5) - x^2 = 11
10x - 10 - x^2 = 11
-x^2 + 10x -10 = 11
-x^2 + 10x -21 = 0
x^2 - 10x + 21 = 0
(x - 7)(x - 3) = 0
x = 7, y = 30
x = 3, y = 10
The third angle is 180-55-65 = 60°.
Exterior angles are 180-55 = 125°, 135°, 120°
(a.) is the answr. ............................................
