A polygon has 377 diagonals, determine the number of sides of this polygon.A27B28C29D30

The number of diagonals in a polygon can be calculated using the formula: n(n-3)/2, where n is the number of sides.

So, if a polygon has 377 diagonals, we can set up the equation:

n(n-3)/2 = 377

Solving this equation for n will give us the number of sides of the polygon.

First, multiply both sides by 2 to get rid of the fraction:

n(n-3) = 754

Then, distribute the n:

n^2 - 3n = 754

Rearrange the equation to set it equal to zero (this is a quadratic equation):

n^2 - 3n - 754 = 0

Now, we can solve this quadratic equation for n. The solutions to a quadratic equation are given by the formula:

n = [-b ± sqrt(b^2 - 4ac)] / (2a)

In this case, a = 1, b = -3, and c = -754. Plugging these values into the quadratic formula gives:

n = [3 ± sqrt((-3)^2 - 41(-754))] / (2*1) n = [3 ± sqrt(9 + 3016)] / 2 n = [3 ± sqrt(3025)] / 2 n = [3 ± 55] / 2

This gives two possible solutions: n = 58/2 = 29 or n = -52/2 = -26.

Since the number of sides of a polygon cannot be negative, the number of sides of the polygon is 29.

So, the correct answer is C29.