10 pts + brainliest for best answer. answer quickly.

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

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°