Two angles of a polygon are right angles and the remaining are `120^@` each. Find the number of sides in it.

Options

A. `8`
B. `7`
C. `9`
D. `5`

Answer

To solve the problem, we need to find the number of sides \( n \) in a polygon where two angles are right angles (90 degrees each) and the remaining angles are each 120 degrees.

### Step-by-Step Solution:

1. **Understanding the Sum of Interior Angles**:
The formula for the sum of the interior angles of a polygon with \( n \) sides is:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]

2. **Setting Up the Equation**:
In this polygon, we have:
- 2 angles of \( 90^\circ \) (right angles)
- The remaining angles are \( 120^\circ \) each.

Therefore, the total sum of the angles can also be expressed as:
\[ 90^\circ + 90^\circ + (n - 2) \times 120^\circ \]
This simplifies to:
\[ 180^\circ + (n - 2) \times 120^\circ \]

3. **Equating the Two Expressions**:
Now, we can set the two expressions for the sum of the interior angles equal to each other:
\[ 180^\circ + (n - 2) \times 120^\circ = (n - 2) \times 180^\circ \]

4. **Expanding and Simplifying**:
Expanding both sides gives:
\[ 180 + 120n - 240 = 180n - 360 \]
Simplifying this, we get:
\[ 120n - 60 = 180n - 360 \]

5. **Rearranging the Equation**:
Rearranging the equation to isolate \( n \):
\[ 360 - 60 = 180n - 120n \]
This simplifies to:
\[ 300 = 60n \]

6. **Solving for \( n \)**:
Dividing both sides by 60 gives:
\[ n = \frac{300}{60} = 5 \]

### Conclusion:
The number of sides in the polygon is \( n = 5 \).