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This is a geometric problem involving angles within a figure that appears to be made up of a parallelogram and a triangle. Let's break down the situation:

1. **Parallel Lines and Transversal**: 
   - The parallel arrows on the sides indicate that the opposite sides of the quadrilateral are parallel, meaning this shape is likely a parallelogram.
   - In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (i.e., they add up to 180°).

2. **Given Angles**:
   - The angle labeled 63° and the one labeled 45° are given.
   - The angles labeled as \(x\) and \(y\) need to be determined.

Let's start with solving for \(x\) and \(y\):

### Step 1: Solving for \(x\)
- Since opposite angles of a parallelogram are equal, the angle adjacent to the angle labeled \(x\) on the same straight line will be equal to the given 63° (these are alternate interior angles because of the transversal).
- Therefore, we use the fact that supplementary angles add up to 180°:
  \[
  x + 63° = 180°
  \]
  Solving for \(x\):
  \[
  x = 180° - 63° = 117°
  \]

### Step 2: Solving for \(y\)
- \(y\) is part of a triangle. The interior angles of a triangle always sum to 180°. The angles in this triangle are 45°, \(y\), and the angle adjacent to \(y\), which is equal to \(63°\) (since it's also an alternate interior angle to the given 63° angle on the left side).
  \[
  y + 45° + 63° = 180°
  \]
  Solving for \(y\):
  \[
  y = 180° - 45° - 63° = 72°
  \]

### Final Results:
- \(x = 117°\)
- \(y = 72°\)

Would you like a detailed explanation of any specific steps? 

Here are five related questions for further practice:
1. What are the properties of angles in a parallelogram?
2. How do alternate interior angles work with parallel lines?
3. What is the sum of the interior angles of a triangle?
4. If one angle of a parallelogram is 90°, what kind of parallelogram is it?
5. Can a parallelogram have all angles equal? If so, what is it called?

**Tip**: In any polygon, the sum of the interior angles can be calculated by the formula \((n-2) \times 180^\circ\), where \(n\) is the number of sides.

Given a parallelogram and triangle with specified angles (63° and 45°), find the unknown angles x and y.

Learn how to solve for unknown angles in a figure consisting of a parallelogram and triangle. This problem involves using the properties of parallelograms and the sum of interior angles in triangles. Suitable for students in Grades 8-10.

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