https://file.aiquickdraw.com/mathbot/file/1727361710146iqd4be44.jpg

Let's analyze the geometry problem in the image.

### Given:
- The diagram represents a parallelogram \( ABCD \), where \( CDE \) is a straight line, and \( AD = DE \).
- A variety of angles are marked on the diagram, and we're asked to solve for:
  - \( \angle x \) in part (a).
  - \( \angle y \) in part (b).

### Part (a) - Find \( \angle x \):
From the diagram, it seems that \( \angle x \) lies on a straight line, so we can apply the property that angles on a straight line sum up to 180°.

Looking at the provided steps:
1. The calculation for \( \angle x \) is based on the fact that angles on the straight line add up to 180°.
   - Given the adjacent angle as 49°, the equation becomes:
   \[
   \angle x = 180^\circ - 49^\circ = 131^\circ
   \]
So, \( \boxed{131^\circ} \) is the value of \( \angle x \).

### Part (b) - Find \( \angle y \):
\( \angle y \) is marked within the parallelogram \( ABCD \), and there is a known angle of 82° at \( B \). From the properties of a parallelogram, opposite angles are equal. Since \( ABCD \) is a parallelogram:
\[
\angle B + \angle D = 180^\circ
\]
This means:
\[
\angle y = 180^\circ - 82^\circ = 98^\circ
\]
Thus, \( \boxed{98^\circ} \) is the value of \( \angle y \).

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Would you like more details on these calculations, or do you have any further questions?

Here are five relative questions to extend your understanding:
1. How do the properties of parallelograms help in solving this problem?
2. What are supplementary angles, and why are they important in this scenario?
3. How can the sum of angles around a point be used in geometric problems?
4. Can this method of finding angles be applied to other quadrilaterals, such as trapezoids?
5. What are alternate interior angles, and do they apply in this case?

### Tip:
When working with polygons, always consider the properties like opposite angles, adjacent angles, and supplementary angles, which are often crucial for solving angle-related problems.

In the diagram below, not drawn to scale, ABCD is a parallelogram. CDE is a straight line and AD = DE. Find angle x and angle y.

Solve a geometry problem involving angles in a parallelogram ABCD with a straight line CDE. Learn how to apply the angle sum property and theorems of parallelograms to find angles x and y, with step-by-step explanations. Ideal for students in Grades 8-10.

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