SOLUTION: The three angles in a triangle always add up to 180 degrees. In a triangle,one angle measures 32 degrees and the second angle is 5 times larger than the third angle. Find the measu

Algebra ->  Triangles -> SOLUTION: The three angles in a triangle always add up to 180 degrees. In a triangle,one angle measures 32 degrees and the second angle is 5 times larger than the third angle. Find the measu      Log On


   

Question 541014: The three angles in a triangle always add up to 180 degrees. In a triangle,one angle measures 32 degrees and the second angle is 5 times larger than the third angle. Find the measures of the angles.
So far I have:
32+x+5x=180
32+6x=180
6x=148
When I divide by 6 I get a decimal answer, I don't know what I'm doing wrong.
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
32+x+5x=180
32+6x=180
6x=148
Instead of getting a decimal, get an improper fraction instead:

Divide both sides by 6, by putting 6 under each side:

6x%2F6 = %28148%2F6%29°  

Reduce the fraction

x = %2874%2F3%29°

Change the improper fraction to a mixed number:

x = %2824%262%2F3%29°

There are 60 minutes in a degree.

Convert the 2%2F3 to minutes by multiplying 2%2F3 times 60',
getting 40', so the answer is

 x =  24°40' = third angle
5x = 120°200' = second angle, but we need to simplify that.

We convert 200 minutes to degrees by diving by 60

200%2F60 = 3%2620%2F60 = 3%261%2F3

So we add 3 to the number of degrees getting 123°, 
and we convert the 1%2F3 to minutes by multiplying by 60,
getting 20'.  

Second angle = 123°20' 

Edwin