The given diagram shows two triangles with several marked angles. We are asked to find the values of $x$ and $y$. Let's work through the steps.

Step 1: Analyze the angles

1. In the top triangle, the three interior angles are:

   • $148^\circ$ (given),
   • $18^\circ$ (given),
   • $(5x - y)^\circ$ (unknown).

   Since the sum of the interior angles of any triangle equals $180^\circ$, we can write the equation for the first triangle: $148^\circ + 18^\circ + (5x - y)^\circ = 180^\circ$ Simplifying this equation: $166^\circ + (5x - y)^\circ = 180^\circ$ 5x - y = 14 \tag{1}

2. In the bottom triangle, the three interior angles are:

   • $(3x + y)^\circ$ (unknown),
   • Two right angles, both $90^\circ$ (since the small square in the corner indicates a right angle).

   Again, using the fact that the sum of the angles in a triangle is $180^\circ$: $(3x + y)^\circ + 90^\circ + 90^\circ = 180^\circ$ Simplifying: $3x + y + 180^\circ = 180^\circ$ 3x + y = 0 \tag{2}

Step 2: Solve the system of equations

We now have the system of equations:

1. $5x - y = 14$
2. $3x + y = 0$

To solve this:

• Add equations (1) and (2): $(5x - y) + (3x + y) = 14 + 0$ $8x = 14$ $x = \frac{14}{8} = 1.75$

• Substitute $x = 1.75$ into equation (2): $3(1.75) + y = 0$ $5.25 + y = 0$ $y = -5.25$

Final Answer:

• $x = 1.75$
• $y = -5.25$

Would you like any further explanation or have questions on this? Here are five related problems you might find interesting:

1. How do you solve a system of equations with more complex terms?
2. What are other methods to solve systems of linear equations besides substitution?
3. Can this method be applied to quadrilaterals and their interior angles?
4. How do angles behave in more irregular polygons (like pentagons)?
5. What is the importance of identifying right angles in geometrical problems?

Tip: Always remember that the sum of angles in any triangle is $180^\circ$.