Is it possible to have a regular polygon each of whose interior angles is `100^(@)` ?

Options

A. No
B. Yes
C. Can not determine
D. None of these

Answer

To determine if it is possible to have a regular polygon where each interior angle measures \(100^\circ\), we can follow these steps:

### Step 1: Use the formula for the interior angle of a regular polygon.
The formula for the interior angle \(A\) of a regular polygon with \(n\) sides is given by:
\[ A = \frac{(n-2) \times 180}{n} \]
We want to find out if \(A = 100^\circ\).

### Step 2: Set up the equation.
Substituting \(100\) for \(A\) in the formula, we get:
\[ 100 = \frac{(n-2) \times 180}{n} \]

### Step 3: Multiply both sides by \(n\) to eliminate the fraction.
\[ 100n = (n-2) \times 180 \]

### Step 4: Expand the right side.
\[ 100n = 180n - 360 \]

### Step 5: Rearrange the equation.
Now, we will move all terms involving \(n\) to one side:
\[ 100n - 180n = -360 \]
This simplifies to:
\[ -80n = -360 \]

### Step 6: Solve for \(n\).
Dividing both sides by \(-80\):
\[ n = \frac{360}{80} = 4.5 \]

### Step 7: Interpret the result.
Since \(n = 4.5\) is not a whole number, it indicates that a regular polygon cannot have \(100^\circ\) as each of its interior angles.

### Conclusion:
Thus, it is not possible to have a regular polygon where each interior angle measures \(100^\circ\).

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