The sum of two numbers is 51. if one fourth of one number exceeds one fifth of another number by 6, which of the following is the smaller number?

Let x=smaller number 
Then x+5=larger number 
Now we are told the following: 
1/5(x+x+5)=x-5 multiply each side by 5 
x+x+5=5x-25 subtract 5x and also 5 from both sides 
x+x+5-5-5x=5x-5x-25-5 collect like terms
-3x=-30 divide both sides by -3
x=10 smaller number 
x+5=10+5=15  larger number 
CK 
1/5(10+15)=10-5 
1/5(25)=10-5
5=5 

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.