What is the radius of x^2 + y^2 -2x -4y -31 = 0

First we have to complete the square on both the x and y terms. Move the 31 to the right side.
x^2 - 2x + y^2 - 4y = 31
x^2 - 2x + 1 + y^2 - 4y + 4 = 31 + 1 + 4
(x - 1)^2 + (y - 2)^2 = 36
36 = r^2
r = 6

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°