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### Problem 1:
**Given:** Two consecutive angles \( AOB \) and \( BOC \), with \( m \angle AOC + m \angle BOC = 120^\circ \). Find \( m \angle XOC \) where \( OX \) is the bisector of \( \angle AOB \).

1. We know that \( m \angle AOC + m \angle BOC = 120^\circ \).
2. Assume \( m \angle AOB = x \) and \( m \angle BOC = 120^\circ - x \).
3. Since \( OX \) is the bisector of \( \angle AOB \), \( m \angle XOB = \frac{x}{2} \).

Let's find \( m \angle XOC \).

### Problem 2:
**Given:** Three consecutive angles \( AOB \), \( BOC \), and \( COD \), such that \( m \angle AOB = 18^\circ \) and \( m \angle COD = 24^\circ \). Calculate the angle formed by the bisectors of \( \angle AOC \) and \( \angle BOD \).

### Problem 3:
**Find:** The value of \( x \) in the diagram where \( \angle AOB = 30^\circ \), \( \angle BOC = 20^\circ \), and we are asked to calculate \( x \).

I will solve these problems now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can still guide you through the steps to solve these problems manually if you'd like. Would you like me to walk you through the solutions or provide further assistance?

In the meantime, here are five related questions to practice:

1. How do you calculate the angle bisector of a given angle?
2. If two consecutive angles sum to \(120^\circ\), how do you determine their individual values?
3. How do you apply the angle bisector theorem to find unknown angles?
4. What is the relationship between consecutive angles on a straight line?
5. How do you calculate the sum of interior angles for a polygon?

**Tip:** When dealing with consecutive angles, remember that angles on a straight line always sum up to \(180^\circ\).

Dados los ángulos consecutivos AOB y BOC, se sabe que m < AOC + m < BOC = 120°. Halla m < XOC si OX es bisectriz del ángulo AOB. También, calcula el ángulo formado por las bisectrices de los ángulos AOC y BOD, y el valor de x en la figura.

Learn how to solve geometric problems involving angle bisectors and consecutive angles, including calculating unknown angles and bisector angles with step-by-step solutions. Suitable for Grades 9-11.

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