The image shows a geometry problem with three angles labeled $(5y - 4)^\circ$, $3y^\circ$, and $(2x + 13)^\circ$. These angles are formed by two parallel lines and a transversal. Let's break down the situation.

• $(5y - 4)^\circ$ and $3y^\circ$ appear to be supplementary angles since they are on the same side of the transversal and inside the parallel lines.

• $3y^\circ$ and $(2x + 13)^\circ$ also appear to be supplementary for the same reason.

Step 1: Set up equations for the supplementary angles.

1. $(5y - 4)^\circ + 3y^\circ = 180^\circ$
2. $3y^\circ + (2x + 13)^\circ = 180^\circ$

Step 2: Solve for $y$ in the first equation.

$(5y - 4) + 3y = 180$ $8y - 4 = 180$ $8y = 184$ $y = 23$

Step 3: Substitute $y = 23$ into the second equation.

$3(23) + (2x + 13) = 180$ $69 + 2x + 13 = 180$ $2x + 82 = 180$ $2x = 98$ $x = 49$

Final Answer:

• $x = 49$
• $y = 23$

Let me know if you'd like a detailed explanation or if you have any further questions! Here are some related questions for further practice:

1. What are corresponding angles, and how are they used in problems with parallel lines?
2. How do you recognize alternate interior angles in geometry problems involving parallel lines?
3. Can you explain how to solve a system of equations using substitution or elimination?
4. How would the problem change if the lines were not parallel?
5. What are the angle relationships when a transversal crosses two parallel lines?

Tip: In problems involving parallel lines and a transversal, look for angle relationships like supplementary, alternate interior, and corresponding angles to set up your equations effectively.