The number of diagonals of a convex polygon is 35. How many sides does the polygon have?

To find the number of sides of a convex polygon given the number of diagonals, you can use the following formula: Number of Diagonals = n(n-3)/2 Where "n" represents the number of sides of the polygon. In your case, you are given that the number of diagonals is 35: 35 = n(n-3)/2 Now, solve for "n": 2 * 35 = n(n-3) 70 = n(n-3) Now, you want to find two numbers whose product is 70, and one of them is 3 more than the other. Those two numbers are 10 and 7 because 10 * 7 = 70, and 10 is 3 more than 7. So, n = 10 (the number of sides of the polygon). Therefore, the convex polygon has 10 sides.