https://file.aiquickdraw.com/mathbot/file/1725547168065tck9z5ra.jpg

The image you provided shows a parallelogram with some angles and a variable \( y \) to solve for. From the visible part of the diagram:

- The angle on the left is labeled as \( 42^\circ \).
- The angles on the top and bottom appear to be the internal angles of the parallelogram.
- The opposite sides of the parallelogram are parallel, which suggests that we can use the properties of parallelograms to solve for the unknowns.

Let me guide you through solving for \( y \):

### Key Properties of Parallelograms:
1. Opposite angles are equal.
2. Adjacent angles are supplementary (i.e., they sum up to \( 180^\circ \)).

### Steps to Solve for \( y \):
- The angle adjacent to the \( 42^\circ \) angle should be \( 180^\circ - 42^\circ = 138^\circ \) because adjacent angles in a parallelogram are supplementary.
- Since opposite angles in a parallelogram are equal, the angle marked \( y \) should be equal to the adjacent angle, i.e., \( y = 138^\circ \).

Therefore, \( y = 138^\circ \).

Let me know if you would like further details or if you have any questions!

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**Related Questions:**
1. How do you calculate the area of a parallelogram?
2. Can a parallelogram have four right angles?
3. What is the sum of the interior angles of any quadrilateral?
4. How do opposite sides in a parallelogram compare in length?
5. What is the relationship between the diagonals of a parallelogram?

**Tip:** Always use properties like symmetry and angle relationships to simplify geometry problems in figures like parallelograms.

What is the value of y in the parallelogram shown in the image, where one angle is labeled 42°?

Learn how to calculate the unknown angle y in a parallelogram when one angle is given as 42°. This geometry problem uses the properties of parallelograms, where adjacent angles are supplementary. Suitable for students in Grades 6-8.

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