STATEMENT-1 : If the angle of a convex polygon are in A.P. ` 120^(@) , 125^(@) , 130^(@)` …, then it has 16 sides and
STATEMENT-2 : The sum of the angles of a polygon of x sides is `(n -2) 180^(@)`

Options

A. Statement-1 is True , Statement-2 is True, Statement -2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True, Statement -2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Stetement-2 is False.
D. Statement-1 is False, Statement-2 is True

Answer

To solve the problem, we will analyze both statements and prove their validity step by step.

### Step 1: Understanding the Angles of the Polygon
The angles of the convex polygon are given in an arithmetic progression (A.P.) as follows:
- First angle (A) = 120°
- Second angle = 125°
- Third angle = 130°
- Common difference (d) = 5°

### Step 2: Finding the Number of Sides (N)
The formula for the sum of the interior angles of a polygon with N sides is:
\[ \text{Sum of angles} = (N - 2) \times 180° \]

### Step 3: Sum of Angles in A.P.
The sum of the angles in A.P. can be calculated using the formula for the sum of an A.P.:
\[ S_N = \frac{N}{2} \times (2A + (N - 1)D) \]
Substituting the values:
- A = 120°
- D = 5°

Thus, we have:
\[ S_N = \frac{N}{2} \times (2 \times 120 + (N - 1) \times 5) \]
\[ S_N = \frac{N}{2} \times (240 + 5N - 5) \]
\[ S_N = \frac{N}{2} \times (5N + 235) \]
\[ S_N = \frac{5N^2 + 235N}{2} \]

### Step 4: Setting the Two Expressions for the Sum Equal
Now, we equate the two expressions for the sum of the angles:
\[ \frac{5N^2 + 235N}{2} = (N - 2) \times 180 \]

### Step 5: Simplifying the Equation
Multiply both sides by 2 to eliminate the fraction:
\[ 5N^2 + 235N = 2(N - 2) \times 180 \]
\[ 5N^2 + 235N = 360N - 720 \]

### Step 6: Rearranging the Equation
Rearranging gives us:
\[ 5N^2 + 235N - 360N + 720 = 0 \]
\[ 5N^2 - 125N + 720 = 0 \]

### Step 7: Dividing by 5
To simplify, divide the entire equation by 5:
\[ N^2 - 25N + 144 = 0 \]

### Step 8: Solving the Quadratic Equation
Using the quadratic formula \( N = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):
Here, \( a = 1, b = -25, c = 144 \):
\[ N = \frac{25 \pm \sqrt{(-25)^2 - 4 \times 1 \times 144}}{2 \times 1} \]
\[ N = \frac{25 \pm \sqrt{625 - 576}}{2} \]
\[ N = \frac{25 \pm \sqrt{49}}{2} \]
\[ N = \frac{25 \pm 7}{2} \]

Calculating the two possible values:
1. \( N = \frac{32}{2} = 16 \)
2. \( N = \frac{18}{2} = 9 \)

### Conclusion for Statement 1
Since we are looking for a convex polygon with angles in A.P. and we found \( N = 16 \), Statement 1 is **True**.

### Step 9: Validating Statement 2
Statement 2 states that the sum of the angles of a polygon with \( N \) sides is given by \( (N - 2) \times 180° \). This is a well-known formula in geometry for polygons, hence Statement 2 is also **True**.

### Final Answer
Both statements are true.

---