https://file.aiquickdraw.com/mathbot/file/1726970318784bp847p1q.jpg

In a rhombus, opposite angles are always equal, and the sum of the interior angles of any quadrilateral is \(360^\circ\).

From the image:
- One angle is given as \(98^\circ\), which means the opposite angle \(z\) will also be \(98^\circ\).
- Since the angles opposite are equal, we have \(x = z = 98^\circ\).
- Now, to find the remaining angles, \(x\) and \(y\), we use the fact that adjacent angles in a rhombus are supplementary, meaning they add up to \(180^\circ\).

Thus,
\[
x + y = 180^\circ
\]
Substituting \(x = 98^\circ\),
\[
98^\circ + y = 180^\circ
\]
Solving for \(y\),
\[
y = 180^\circ - 98^\circ = 82^\circ
\]

Therefore:
- \(x = 98^\circ\)
- \(y = 82^\circ\)
- \(z = 98^\circ\)

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How do the properties of a rhombus differ from a general parallelogram?
2. What would change if this were a square instead of a rhombus?
3. How can the angles of a rhombus be used to calculate its diagonals?
4. How are the diagonals of a rhombus related to its angles?
5. Can a rhombus have right angles? Why or why not?

**Tip**: In a rhombus, diagonals bisect each other at right angles, and they also bisect the rhombus's interior angles.

Find the measure of the three missing angles in the rhombus below.

Learn how to find the missing angles in a rhombus using key geometric properties. This problem involves understanding the angle sum property of a quadrilateral and the properties of a rhombus, making it ideal for students in Grades 6-8.

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