If PQRS is a rhombus and `/_SPQ = 50^@`, then `/_RSQ` is

Options

A. `55^@`
B. `65^@`
C. `75^@`
D. `45^@`

Answer

To solve the problem, we need to find the measure of angle \( \angle RSQ \) in the rhombus \( PQRS \) given that \( \angle SPQ = 50^\circ \).

### Step-by-Step Solution:

1. **Understanding the Properties of a Rhombus**:
- A rhombus has all four sides equal.
- The opposite angles of a rhombus are equal.
- The diagonals of a rhombus bisect each other at right angles.

2. **Identify Given Information**:
- We are given that \( \angle SPQ = 50^\circ \).

3. **Using the Diagonal Property**:
- In a rhombus, the diagonal \( PQ \) bisects the angles at vertices \( P \) and \( S \).
- Therefore, \( \angle SPQ \) is half of \( \angle RPQ \).
- This means:
\[ \angle RPQ = 2 \times \angle SPQ = 2 \times 50^\circ = 100^\circ \]

4. **Finding \( \angle RSQ \)**:
- Since the opposite angles in a rhombus are equal, we have:
\[ \angle RPQ = \angle RSQ \]
- Therefore:
\[ \angle RSQ = 100^\circ \]

5. **Conclusion**:
- The measure of angle \( \angle RSQ \) is \( 100^\circ \).

### Final Answer:
\[ \angle RSQ = 100^\circ \]