Answer :
Sum of all angles in a triangle is 180 degrees. If we mark angles as a, b and c, from given ratio we would have:
a + b + c = 180
a = 2x
b = 4x
c = 9x
2x + 4x + 9x =180
15x = 180
x = 12
a = 2x = 24
b = 4x = 48
c = 9x = 118
[tex]2:4:9\to2+4+9=15\\\\the\ sum\ of\ angles\ is\ equal\ 180^o\\\\180^o:15=12^o\\\\therefore\ the\ measures\ of\ the\ angles\ of\ \Delta RTS\ are\ equal:\\\\m\angle R=2\cdot12^o=24^o\\\\m\angle T=4\cdot12^o=48^o\\\\m\angle S=9\cdot12^o=108^o[/tex]
