Focus solely on triangle RTS. If needed, erase the portion that extends out toward point U If we focus on the triangle only, then angle R = angle T since they are the base angles of the isosceles triangle. We know that triangle RST is isosceles since RS = ST is given to us.
Because angle R = angle T, we know angle R = 180-15x angle T = 180-15x and we also know angle S = 4x+2 since that's given as well
Add up the three angles and set that sum equal to 180. Then solve for x R+S+T = 180 (180-15x)+(4x+2)+(180-15x) = 180 (-15x+4x-15x) + (180+2+180) = 180 -26x + 362 = 180 -26x + 362-362 = 180-362 -26x = -182 -26x/(-26) = -182/(-26) x = 7
