A regular polygon has two of its consecutive diagonals as the lines `sqrt(3)x+y-sqrt(3)` and `2y=sqrt(3)` . Point `(1,c)` is one of its vertices. Find the equation of the sides of the polygon and also find the coordinates of the vertices.

Explanation

To solve the problem, we need to find the equations of the sides of a regular polygon given two of its consecutive diagonals and a vertex. Let's break down the solution step by step.

### Step 1: Identify the given lines
The two consecutive diagonals are given as:
1. \( \sqrt{3}x + y - \sqrt{3} = 0 \) (let's call this Line 1)
2. \( 2y = \sqrt{3} \) or \( y = \frac{\sqrt{3}}{2} \) (let's call this Line 2)

### Step 2: Find the angle between the diagonals
...