Question 574560
<pre>
When you want to split a number N up into three parts 
in the ratio of P:Q:R, the three parts are:

1st part: {{{P/(P+Q+R)}}}·N
2nd part: {{{Q/(P+Q+R)}}}·N
3rd part: {{{R/(P+Q+R)}}}·N

You know that the sum of the three angles in any triangle
is 180°.

So you want to split N=180° up into three parts 
in the ratio of 8:3:4, so
P=8, Q=3, R=4

1st part: {{{8/(8+3+4)}}}·180° = {{{8/15}}}·180° = 96° 
2nd part: {{{3/(8+3+4)}}}·180° = {{{3/15}}}·180° = 36°
3rd part: {{{4/(8+3+4)}}}·180° = {{{4/15}}}·180° = 48°

The smallest of those three is 36°.

[As a check we add those three: 96°+36°+48°= 180°]

Edwin</pre>