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In the given figure, lines \( o \parallel h \), and we need to find the values of \( x \) and \( z \).

We will apply the concept of parallel lines and the angles formed by a transversal:

1. **Corresponding Angles**: Since \( o \parallel h \) and the transversal intersects both lines, the angle \( x^\circ \) is equal to the given \( 74^\circ \) by the property of corresponding angles.

    Thus, we have:
    \[
    x = 74^\circ
    \]

2. **Linear Pair**: The angles on a straight line sum to \( 180^\circ \). Therefore, the sum of \( (3z - 1)^\circ \) and \( x^\circ \) must be \( 180^\circ \).

    So, the equation is:
    \[
    (3z - 1) + 74 = 180
    \]
    Simplifying:
    \[
    3z - 1 + 74 = 180
    \]
    \[
    3z + 73 = 180
    \]
    \[
    3z = 180 - 73
    \]
    \[
    3z = 107
    \]
    \[
    z = \frac{107}{3} \approx 35.67^\circ
    \]

Thus, the values are:
- \( x = 74^\circ \)
- \( z \approx 35.67^\circ \)

Would you like further clarification or details?

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Here are 5 related questions to expand on the topic:
1. What is the corresponding angle postulate for parallel lines?
2. How do you find the value of an unknown angle using a linear pair?
3. What are alternate interior angles, and how do they relate to parallel lines?
4. Can the sum of the angles on a straight line be more than 180°?
5. What are the steps to solve equations with multiple variables?

**Tip:** When solving for angles involving parallel lines, always look for relationships like corresponding angles, alternate interior angles, or linear pairs.

In the figure below, o || h. Find the values of x and z.

Learn how to find the values of angles x and z using the corresponding angles and linear pair properties in a figure with parallel lines. This problem covers key concepts in geometry for students in Grades 9-10.

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