How many sides does a polygon have if the sum of its interior angles is 30 right angles ?

Options

A. 15
B. 17
C. 19
D. 20

Answer

To find the number of sides \( n \) of a polygon given that the sum of its interior angles is 30 right angles, we can follow these steps:

### Step 1: Understand the relationship between sides and interior angles
The formula for the sum of the interior angles \( S \) of a polygon with \( n \) sides is given by:
\[ S = 180(n - 2) \]
where \( n \) is the number of sides.

### Step 2: Convert the given information
We know that the sum of the interior angles is 30 right angles. Since one right angle is \( 90^\circ \), we can convert 30 right angles into degrees:
\[ 30 \text{ right angles} = 30 \times 90^\circ = 2700^\circ \]

### Step 3: Set up the equation
Now we can set up the equation using the formula for the sum of the interior angles:
\[ 180(n - 2) = 2700 \]

### Step 4: Solve for \( n \)
To find \( n \), we first divide both sides by 180:
\[ n - 2 = \frac{2700}{180} \]
Calculating the right side:
\[ \frac{2700}{180} = 15 \]
So we have:
\[ n - 2 = 15 \]
Now, add 2 to both sides:
\[ n = 15 + 2 = 17 \]

### Conclusion
The polygon has **17 sides**.

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