Let's break this down step by step, like I'm teaching it to a kid.

1. Understanding the Problem

• There’s a parallelogram (a shape where opposite sides are equal and parallel).
• Two angles are labeled: one is $115^\circ$ and the other is marked with $x^\circ$.
• You need to find out what $x$ and another angle $y$ are.

2. Angle Relationships in a Parallelogram

• In a parallelogram:
  • Opposite angles are equal.
  • Adjacent angles (angles next to each other) add up to 180°.

3. Finding $x$

• Step 1: Look at the given $115^\circ$ angle.

  • The angle next to it (let’s call it $x$) must add up with $115^\circ$ to make $180^\circ$, because they are adjacent in the parallelogram.

  • So, $115^\circ + x = 180^\circ$.

• Step 2: Solve for $x$.

  • Subtract $115^\circ$ from $180^\circ$: $x = 180^\circ - 115^\circ = 65^\circ$
  • So, $x = 65^\circ$.

4. Finding $y$

• $y$ is an angle opposite to the $x^\circ$ angle you just found.
• Since opposite angles in a parallelogram are equal:
  • $y = 65^\circ$.

5. Summary

• $x = 65^\circ$
• $y = 65^\circ$

These values satisfy the properties of a parallelogram, making sure that adjacent angles add up to 180° and opposite angles are equal.

Would you like more details or have any questions about this?

Here are some questions to expand your understanding:

1. What would happen if one of the angles was 90°?
2. How would the solution change if the shape was not a parallelogram?
3. Why do the angles in a parallelogram add up to 180° when they are adjacent?
4. What is the difference between adjacent and opposite angles?
5. How do the properties of a parallelogram help us solve for unknown angles?

Tip: Remember, adjacent angles in parallelograms always add up to 180°, which is a handy trick for solving these problems!