Step 1: Define the Given Information
We are given that the interior angles of a polygon are in arithmetic progression (A.P.) with a common difference of 6° and the largest angle is 219°.
The sum of the interior angles of an \( n \)-sided polygon is given by: \[ \frac{n}{2} \left( 2a + (n-1) \times 6 \right) = (n-2) \times 180 \] where \( a \) is the first angle. Simplifying: \[ an + 3n^2 - 3n = (n-2) \times 180 \]
Step 2: Apply the Condition for the Largest Angle
We are also given that the largest interior angle is 219°, which gives the equation: \[ a + (n-1) \times 6 = 219 \] Simplifying this equation: \[ a = 225 - 6n \]
Step 3: Substitute into the Sum Equation
Now, substitute the value of \( a = 225 - 6n \) into the sum equation: \[ (225 - 6n) + 3n^2 - 3n = (n-2) \times 180 \] Simplifying and solving this quadratic equation, we get: \[ n = 20 \]
Final Answer: \( n = 20 \)
20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol$^{-1}$)