Question

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

Answer 1

well, since we know the sum of all angles will be 180°, then let's divide 180 by (2 + 4 + 9) and distribute accordingly to each angle.

`\stackrel{R}{2}~~ : ~~\stackrel{S}{4}~~ : ~~\stackrel{T}{9}\qquad \implies \qquad \stackrel{R}{2\cdot (180)/(2+4+9)}~~ : ~~\stackrel{S}{4\cdot (180)/(2+4+9)}~~ : ~~\stackrel{T}{9\cdot (180)/(2+4+9)} \\\\\\ \stackrel{R}{2\cdot 12}~~ : ~~\stackrel{S}{4\cdot 12}~~ : ~~\stackrel{T}{9\cdot 12}\qquad \implies \qquad \stackrel{R}{24^o}~~ : ~~\stackrel{S}{48^o}~~ : ~~\stackrel{T}{108^o}`