m∠AOC = m∠AOB + m∠BOC
We have m∠AOC = 19°, m∠AOB = 4x - 15 and m∠BOC = 2x + 10. Substitute:
19 = (4x - 15) + (2x + 10)
19 = (4x + 2x) + (-15 + 10)
19 = 6x - 5 add 5 to both sides
24 = 6x divide both sides by 6
4 = x
m∠BOC = 2x + 10 → m∠BOC = 2(4) + 10 = 8 + 10 = 18
m∠AOB = 4x - 15 → m∠AOB = 4(4) - 15 = 16 - 15 = 1
Answer: c. m∠BOC = 18°, m∠AOB = 1°
