If `P Q R S` is a square, then write the measure of `/_S R P`

Options

A. `90^@`
B. `45^@`
C. `40^@`
D. `50^@`

Answer

To find the measure of angle \( \angle SRP \) in square \( PQRS \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of a Square**:
- In a square, all sides are equal and all angles are \( 90^\circ \).

2. **Identify the Diagonal**:
- The diagonal \( PR \) divides the square into two triangles: \( \triangle PSR \) and \( \triangle PQR \).

3. **Recognize the Equal Sides**:
- Since \( PQRS \) is a square, we have \( PS = SR \) (both are sides of the square).

4. **Use the Properties of Isosceles Triangles**:
- In triangle \( PSR \), since \( PS = SR \), the angles opposite these sides are equal. Therefore, \( \angle PSR = \angle SRP \).

5. **Calculate the Angle at \( S \)**:
- Since \( PQRS \) is a square, \( \angle PSR \) is \( 90^\circ \).

6. **Apply the Angle Sum Property**:
- The sum of angles in triangle \( PSR \) is \( 180^\circ \):
\[ \angle PSR + \angle SRP + \angle RSP = 180^\circ \]
- Let \( \angle SRP = x \). Since \( \angle PSR = x \) as well, we can substitute:
\[ x + x + 90^\circ = 180^\circ \]

7. **Solve for \( x \)**:
- Combine like terms:
\[ 2x + 90^\circ = 180^\circ \]
- Subtract \( 90^\circ \) from both sides:
\[ 2x = 90^\circ \]
- Divide by 2:
\[ x = 45^\circ \]

8. **Conclusion**:
- Therefore, the measure of \( \angle SRP \) is \( 45^\circ \).

### Final Answer:
The measure of \( \angle SRP \) is \( 45^\circ \).