Answer:
see explanation
Step-by-step explanation:
∠AOB + ∠BOC = ∠AOC ← substitute values
2x + 8 + 3x + 14 = 7x - 2, that is
5x + 22 = 7x - 2 ( subtract 7x from both sides )
- 2x + 22 = - 2 ( subtract 22 from both sides )
- 2x = - 24 ( divide both sides by - 2 )
x = 12
Thus
∠AOC = 7x - 2 = (7 × 12) - 2 = 84 - 2 = 82°
∠AOB = 2x + 8 = (2 × 12) + 8 = 24 + 8 = 32°
∠BOC = 3x + 14 = (3 × 12) + 14 = 36 + 14 = 50°
