The measure of the smallest angle of a triangle is ​one-third the measure of the largest angle. The measure of the second angle is 65 degrees less than the measure of the largest angle. Find the measure of the angles of the triangle?

word problem

1 Answer
Sep 20, 2017

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!