To solve the problem:

Given:

1. $g \parallel o$: The lines $g$ and $o$ are parallel.
2. Transversal $m$ creates angles $x^\circ$, $83^\circ$, and $(4y - 3)^\circ$.

Key Geometry Principles:

1. Corresponding Angles Postulate: When a transversal intersects two parallel lines, corresponding angles are equal.
2. Linear Pair Property: The sum of angles on a straight line is $180^\circ$.

Step 1: Set up equations for $x$ and $y$

• $x^\circ$ and $83^\circ$ are corresponding angles, so: $x = 83$

• $(4y - 3)^\circ$ and $x^\circ$ form a linear pair, so their sum is $180^\circ$: $x + (4y - 3) = 180$

Step 2: Solve for $y$

• Substitute $x = 83$ into the linear pair equation: $83 + (4y - 3) = 180$ Simplify: $4y + 80 = 180$ $4y = 100$ $y = 25$

Final Solution:

$x = 83, \quad y = 25$

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Expanding Your Learning:

1. What are alternate interior angles, and how do they relate to this problem?
2. How does the Corresponding Angles Postulate apply to non-parallel lines?
3. Can the linear pair property hold for three or more angles?
4. How would this problem change if the parallel lines were not parallel?
5. What are co-interior angles, and how are they used in geometry?

Tip: Practice identifying corresponding, alternate, and co-interior angles to strengthen your understanding of parallel line properties.