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EXPLAIN SIMPLY AND  TEACH LIKE UR EXPLAINING TO A KID

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!

Work out the values of x and y. Justify your answers.

Discover how to find the values of unknown angles in a parallelogram using key geometry concepts. This problem explores the properties of parallelograms and angle relationships, making it ideal for students in Grades 8-10.

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