Two plane mirrors are inclined at some angle `theta`. If a ball is placed between the mirrors and there are 9 images formed for the ball, then angle `theta` may be equal to

Options

A. `45^@`
B. `60^@`
C. `36^@`
D. `90^@`

Explanation

To solve the problem of finding the angle \( \theta \) at which two plane mirrors are inclined, given that they form 9 images of a ball placed between them, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: The total number of images \( n \) formed by two plane mirrors inclined at an angle \( \theta \) can be calculated using the formula:
\[ n = \frac{360}{\theta} - 1 \]

2. **Set Up the Equation**: According to the problem, the number of images formed is 9. Therefore, we can set up the equation:
\[ 9 = \frac{360}{\theta} - 1 \]

3. **Rearrange the Equation**: To isolate \( \theta \), we first add 1 to both sides:
\[ 10 = \frac{360}{\theta} \]

4. **Cross-Multiply**: Now, we can cross-multiply to solve for \( \theta \):
\[ 10\theta = 360 \]

5. **Solve for \( \theta \)**: Divide both sides by 10:
\[ \theta = \frac{360}{10} = 36 \text{ degrees} \]

### Conclusion:
The angle \( \theta \) at which the two mirrors are inclined is \( 36 \) degrees.