A certain tree T or order 35 is known to have 25 vertices of degree 1, two vertices of degree 2, three vertices of degree 4, one vertex of degree 5, and two vertices of degree 6. It also contains two vertices of the same degree x. What is x?

Answer: 10

Step-by-step explanation:

The sum of degrees of vertices of tree is 2n - 2

So let n be the number of vertices and x the unknown

n = 35+x

2 (35+x) - 2 = x + (25*1) + (2*2) + (3*4) + (1*5) + (2*6) + (2 * x)

68+2x=x+58+2x

2x-3x = 58-68

x = 10