SOLUTION: the measure of a 3 angles of the triangle are in the ratio 2:3:4.find the measure of its angle

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Question 514270: the measure of a 3 angles of the triangle are in the ratio 2:3:4.find the measure of its angle
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F9ths of the total of 9.

3 is 3%2F9ths of the total of 9.

4 is 4%2F9ths of the total of 9.

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

we want to know:

1. WHAT is 2%2F9ths of the total of 180°?

2. WHAT is 3%2F9ths (or 1%2F3) of that total of 180°?

3. WHAT is 4%2F9ths of the total of 180°?

The answer to the first one,

"WHAT is 2%2F9ths of the total of 180°?"

is found simply by multiplying by that fraction

2%2F9·180° = 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