Question

Angles ∆RST are in the ratio 2:4:9 what are the measures of the angles

Answer 1

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

Answer 2

`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`