Question

the sum of the measures of two acute angle is 120.the supplement of the smaller angle is 10 more than six times the complement of the larger angle.find the measures of the two acute angles.

Answer 1

Let's call the angle measures x and y, where y is the larger angle.

The sum of x and y is 120, so
\[x+y=120\]
The supplement of the smaller angle is 180-x
The complement of the larger angle is 90-y
So "the supplement of the smaller angle is 10 more than 6 times the complement of the larger angle" will translate to
\[(180-x)=6(90-y)+10\]
Your two equations are
\[x+y=120\]\[(180-x)=6(90-y)+10\]
Solve the top equation for y, then substitute in the bottom equation, and then solve for x.