If the sum of all interior angles of a regular polygon is 14 right angles, then its number of sides is

Options

A. 8
B. 9
C. 7
D. 6

Answer

To find the number of sides of a regular polygon given that the sum of all interior angles is 14 right angles, we can follow these steps:

### Step 1: Understand the formula for the sum of interior angles
The sum of the interior angles of a polygon with \( n \) sides is given by the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]

### Step 2: Convert right angles to degrees
Since we know that the sum of the interior angles is 14 right angles, we need to convert this into degrees. One right angle is equal to \( 90^\circ \), so:
\[ 14 \text{ right angles} = 14 \times 90^\circ = 1260^\circ \]

### Step 3: Set up the equation
Now we can set up the equation using the formula for the sum of the interior angles:
\[ (n - 2) \times 180^\circ = 1260^\circ \]

### Step 4: Solve for \( n \)
To solve for \( n \), we first divide both sides of the equation by \( 180^\circ \):
\[ n - 2 = \frac{1260^\circ}{180^\circ} \]
Calculating the right side:
\[ n - 2 = 7 \]

Now, add 2 to both sides to find \( n \):
\[ n = 7 + 2 = 9 \]

### Conclusion
Thus, the number of sides of the polygon is:
\[ \boxed{9} \]

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