Triangle word problem

Question

the largest angle of a triangle has a measure that is 10 degrees less than 3 times the measure of the second smallest angle. the measure of the smallest angle is equal to the difference between the measure of the largest angle and twice the measure of the second smallest angle. Determine the measures of the three angles of the triangles. 

Answer 1

L=largest

M=middle

S=smallest

 

L=3M-10

S=L-2M

S+M+L=180

(L-2m)+M+(3M-10)=180

L-2M+M+3M-10=180

L=3M-10

3M-10-2M+M+3M-10=180

5M-20=180

5M=200

M=40º (middle)

L=3*40-10=120-10=110º (largest)

S=110-2*40=110-80=30º (smallest)