Triangle RST is drawn on the coordinate plane with vertices 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'
Let's find the slopes of the sides of triangle RST.
The slope of the side RS can be found using the formula (y2-y1)/(x2-x1) = (-6-0)/(5-5) = undefined.
The slope of the side ST can be found using the formula (y2-y1)/(x2-x1) = (2-0)/(7-5) = 1.
The slope of the side TR can be found using the formula (y2-y1)/(x2-x1) = (2-(-6))/(7-5) = 4.
To translate triangle RST 2 units to the right and 4 units down to create triangle R'S'T', we will add 2 to the x-coordinates and subtract 4 from the y-coordinates of the vertices of triangle RST.
The vertices of triangle R'S'T' are (5+2, -6-4) = (7, -10), (5+2, 0-4) = (7, -4), and (7+2, 2-4) = (9, -2).
The slope of the side R'S' can be found using the formula (y2-y1)/(x2-x1) = (-10-(-4))/(7-7) = undefined.
The slope of the side S'T' can be found using the formula (y2-y1)/(x2-x1) = (-2-(-4))/(9-7) = 1.
The slope of the side T'R' can be found using the formula (y2-y1)/(x2-x1) = (-2-(-10))/(9-7) = 4.
Triangle R'S'T' has one right angle and one angle equal to 45 degrees since the slopes of S'T' and T'R' are both 1.
Therefore, the sum of the angles of triangle R'S'T' is 90 + 45 + 45 = <<90+45+45=180>>180 degrees. Answer: \boxed{180}.