In this problem, we have two parallel lines, $g \parallel o$, and a transversal line $n$ that intersects both of these parallel lines. We are tasked with finding the values of $z$ and $x$ based on the angles provided.

Step-by-Step Solution:

1. Identifying angle relationships:

• The 85° angle and $z^\circ$ angle are alternate interior angles because $g \parallel o$ and $n$ is a transversal. Alternate interior angles are congruent when lines are parallel, so: $z = 85^\circ$

2. Solving for $x$:

• The angle $(6x - 25)^\circ$ is supplementary to the angle $z^\circ$ (since these two form a straight line on the same side of the transversal $n$). Supplementary angles add up to 180°, so: $z + (6x - 25) = 180$ Substituting $z = 85^\circ$: $85 + (6x - 25) = 180$ Simplifying: $85 + 6x - 25 = 180$ $6x + 60 = 180$ $6x = 120$ $x = 20$

Final Answers:

• $z = 85^\circ$
• $x = 20$

Would you like more details on any of these steps, or do you have any questions?

5 Related Questions:

1. What are alternate interior angles, and how are they used in geometry?
2. How do you determine if two angles are supplementary?
3. What are corresponding angles, and how do they differ from alternate interior angles?
4. Can we always use the same reasoning for angles when the lines are not parallel?
5. How do transversal lines affect angle relationships?

Tip:

When working with parallel lines and a transversal, always look for angle relationships like alternate interior angles or corresponding angles. These can greatly simplify solving for unknowns!