Question 514270
<pre>
This could be called a lesson on
COMPARING PARTS TO THE TOTAL IN A PROPORTION:

 2:3:4

Those three numbers in that proportion add up to 9.
The three angles of the triangle we want add up to 180²,

Notice this: 

2 is {{{2/9}}}ths of the total of 9.

3 is {{{3/9}}}ths of the total of 9.

4 is {{{4/9}}}ths of the total of 9.

Similarly, since the angles of a triangle add up to 180°,

we want to know:

1. WHAT is {{{2/9}}}ths of the total of 180°?

2. WHAT is {{{3/9}}}ths (or {{{1/3}}}) of that total of 180°?

3. WHAT is {{{4/9}}}ths of the total of 180°?

The answer to the first one,

"WHAT is {{{2/9}}}ths of the total of 180°?"

is found simply by multiplying by that fraction

{{{2/9}}}·180° = 40°. So that's one of the angles.

The other two angles are found the same way.  You'll 
get 60° and 80° for them.  It checks because they
add up to 180°.

Edwin</pre>