Triangle RST is drawn on the coordinate plane with verticals at (5,-6), (5,0), and (7,2). The triangle is then translated to units to the right and four units down to create triangle R’S’T’. What is the sum of the angles of triangle R’S’T’? The sum of the angles is degrees?
First, let's find the coordinates of R', S', and T' after the translation.
R' will be 1 unit to the right and 4 units down from R, so its coordinates will be (5+1, -6-4) = (6, -10).
S' will also be 1 unit to the right and 4 units down from S, so its coordinates will be (5+1, 0-4) = (6, -4).
T' will be 1 unit to the right and 4 units down from T, so its coordinates will be (7+1, 2-4) = (8, -2).
Now, we can find the lengths of the sides of triangle R'S'T'.
R'S' has a length of sqrt((6-6)^2 + (-10-(-4))^2) = sqrt(0+36) = 6.
S'T' has a length of sqrt((6-8)^2 + (-4-(-2))^2) = sqrt(4+4) = sqrt(8) = 2sqrt(2).
R'T' has a length of sqrt((6-8)^2 + (-10-(-2))^2) = sqrt(4+64) = sqrt(68) = 2sqrt(17).
Thus, triangle R'S'T' is an isosceles triangle with R'S' = S'T'. Therefore, the sum of the angles of triangle R'S'T' is 180 - 180/2 = 180 - 90 = <<180-90=90>>90 degrees. Answer: \boxed{90}.