The interior angle of a regular polygon is `156^0dot` Find the number of sides of the polygon.

Answer

To find the number of sides of a regular polygon given that each interior angle is \(156^\circ\), 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 know that \(A = 156^\circ\).

### Step 2: Set up the equation
Substituting \(156\) for \(A\) in the formula gives us:
\[ 156 = \frac{(n-2) \times 180}{n} \]

### Step 3: Cross-multiply to eliminate the fraction
Cross-multiplying results in:
\[ 156n = (n-2) \times 180 \]

### Step 4: Expand the right side
Expanding the right side of the equation:
\[ 156n = 180n - 360 \]

### Step 5: Rearrange the equation
Now, we will move all terms involving \(n\) to one side:
\[ 156n - 180n = -360 \]
This simplifies to:
\[ -24n = -360 \]

### Step 6: Solve for \(n\)
Dividing both sides by \(-24\):
\[ n = \frac{360}{24} \]

### Step 7: Calculate the value of \(n\)
Calculating the division:
\[ n = 15 \]

### Conclusion
The number of sides of the polygon is \(15\).

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