First let #l# equal the largest angle, #m# equal the medium angle and #s# equal the smallest angle. Then we change the worded question into a mathematical equation. The small angle is #1/3# of the large angle, this means that #s=l/3#. The medium angle is the large angle minus 65, this means #m=l-65#. We now have enough information to solve this question. Since all three angles in a triangle equal 180, we get
#180=l+m+s#. By substituting in the different value for #m# and #s#, we get
#180=l+l-65+l/3#. We now group like terms to get
#180=2l-65+l/3#. Then we add 65 to both sides, so
#245=2l+l/3#. Next we multiply everything by 3, to get
#345=6l+l#. We group all like terms again,
#735=7l#. Finally, we divide both sides by 7, which leave us with
#735/7=l#
#105=l#. Therefore the largest angle is equal to #105^@#.
The last steps are to find the other angles. Since #m=l-65#, we substitute 105 in to get
#m=105-65#
#m=40^@#.
We do the same with #s=l/3# to get
#s=105/3#
#s=35^@#.
I hope I helped!
