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To solve for the missing angles \(x^\circ\), \(y^\circ\), and \(z^\circ\) in the rhombus, we can use the following properties:

1. **All angles in a quadrilateral add up to 360°**.
2. **Opposite angles in a rhombus are equal**.
3. **Adjacent angles in a rhombus are supplementary (add up to 180°)**.

From the image:
- One angle is given as \(78^\circ\) at the bottom left.
- Let the opposite angle at the top right be \(x^\circ\), so \(x^\circ = 78^\circ\) (since opposite angles are equal).
- The adjacent angles \(y^\circ\) and \(z^\circ\) must each satisfy \(78^\circ + z^\circ = 180^\circ\) and \(78^\circ + y^\circ = 180^\circ\) because they are supplementary.

Thus:
- \(z^\circ = 180^\circ - 78^\circ = 102^\circ\)
- \(y^\circ = 180^\circ - 78^\circ = 102^\circ\)

Therefore, the three missing angles are:
- \(x^\circ = 78^\circ\)
- \(y^\circ = 102^\circ\)
- \(z^\circ = 102^\circ\)

Would you like more details on any of the steps? Here are five related questions to expand your understanding:

1. What other properties of rhombuses can help in solving geometry problems?
2. How would this solution change if the given angle was different, like 90° or 120°?
3. How do the properties of parallelograms apply to rhombuses?
4. What is the relationship between the diagonals of a rhombus and its angles?
5. How do you derive the total sum of interior angles for any polygon?

**Tip:** Always remember that opposite angles of a rhombus are equal, and adjacent angles are supplementary. This simplifies the angle calculations significantly!

Find the measure of the three missing angles in the rhombus where one angle is 78°.

Learn how to find the three missing angles in a rhombus where one angle is 78°. This problem involves key geometry concepts, including the properties of quadrilaterals and theorems on rhombuses. Suitable for students in Grades 7-9.

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