Question 992331
<pre>
2:4:3 = A:B:C

{{{2/(2+4+3)=A/(A+B+C)}}}, {{{4/(2+4+3)=B/(A+B+C)}}}, {{{3/(2+4+3)=C/(A+B+C)}}}

and since A+B+C=180°, the above proportions are:

{{{2/9=A/"180°"}}}, {{{4/9=B/"180°"}}}, {{{3/9=C/"180°"}}}

Cross-multiplying,

{{{9A="360°"}}}, {{{9B="720°"}}}, {{{9C="540°"}}}

{{{A="40°"}}}, {{{B="80°"}}}, {{{C="60°"}}}



{{{drawing(200,1600/7,-.2,1.2,-.2,1.4,
locate(0,0,C), locate(1,0,B), locate(.65,1.27,A),
red(arc(0,0,.5,-.5,0,60)),

red(arc(1,0,.5,-.5,105,180)),
locate(.05,.11,"60°"),locate(.8,.11,"80°"), locate(.59,1.05,"40°"),
red(arc(1.347296355cos(60*pi/180),1.347296355sin(60*pi/180),.5,-.5,240,284)),

triangle(1.347296355cos(60*pi/180),1.347296355sin(60*pi/180),

0,0,1,0))}}} 
Edwin</pre>