Is it possible to have a regular polygon whose each interior angle is :
(i) `170^@ (ii) 1370^@`

Answer

To determine if it's possible to have a regular polygon with each interior angle measuring 170 degrees or 1370 degrees, we can use the formula for the interior angle of a regular polygon:

\[ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} \]

where \( n \) is the number of sides of the polygon.

### Step 1: Check for 170 degrees

1. Set the interior angle to 170 degrees:
\[ 170 = \frac{(n - 2) \times 180}{n} \]

2. Multiply both sides by \( n \) to eliminate the fraction:
\[ 170n = (n - 2) \times 180 \]

3. Expand the right side:
\[ 170n = 180n - 360 \]

4. Rearrange the equation to isolate \( n \):
\[ 170n - 180n = -360 \]
\[ -10n = -360 \]

5. Divide both sides by -10:
\[ n = 36 \]

Since \( n = 36 \) is a positive integer, it is possible to have a regular polygon with each interior angle measuring 170 degrees.

### Step 2: Check for 1370 degrees

1. Set the interior angle to 1370 degrees:
\[ 1370 = \frac{(n - 2) \times 180}{n} \]

2. Multiply both sides by \( n \):
\[ 1370n = (n - 2) \times 180 \]

3. Expand the right side:
\[ 1370n = 180n - 360 \]

4. Rearrange the equation to isolate \( n \):
\[ 1370n - 180n = -360 \]
\[ 1190n = -360 \]

5. Divide both sides by 1190:
\[ n = \frac{-360}{1190} \]

Since \( n \) is negative, it is not possible to have a regular polygon with each interior angle measuring 1370 degrees.

### Conclusion
- It is possible to have a regular polygon with each interior angle of 170 degrees (36 sides).
- It is not possible to have a regular polygon with each interior angle of 1370 degrees.