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.