Question

The sum of the measures of the angles of a triangle is 180 . The largest angle measures 10° less than the sum of the 2 others, the measure of the middle size angle is the average of the other 2 find the measures of the 3 angles

Answer 1

let the angles be x,y,z
and x>y>z
x+y+z=180 ...(1)
x=y+z-10
y+z=x+10
x+x+10=180
2x=170
x=85
y+z=180-85=95 ...(2)
also \[y=\frac{ x+z }{ 2 },2y=85+z,z=2y-85 ...(3)\]
put in (2) and solve
and complete.