Question 700143
You are right.
The angles measuring (in degrees) {{{y}}} and {{{x+y+5}}} are supplementary,
so {{{y+(x+y+5)=180}}} --> {{{x+2y+5=180}}} as you wrote.
The angles measuring {{{x+y+5}}} and {{{2x}}} are also supplementary,
so {{{2x+(x+y+5)=180}}} --> {{{3x+y+5=180}}} as you knew.
Those two equations can be simplified a bit.
{{{x+2y+5=180}}} --> {{{x+2y=180-5}}} --> {{{x+2y=175}}}
{{{3x+y+5=180}}} --> {{{3x+y=180-5}}} --> {{{3x+y=175}}}
Then we would have the system of linear equations
{{{system(x+2y=175,3x+y=175)}}}
The solution is {{{highlight(x=35)}}} with {{{highlight(y=70)}}}
The three angle measures would be
{{{highlight(y=70)}}} for the left angle,
{{{2x=2*35=highlight(70)}}} for the right angle, and
{{{x+y+5=35+70+5=highlight(110)}}} for the top angle.
 
ALTERNATE WAYS TO THE SAME SOLUTION:
The left and right angles are vertical angles, so they have the same measure,
and {{{y=2x}}} could be one of your equations.
Then your system could be
{{{system(y=2x,3x+y=175)}}} or {{{system(x+2y=175,y=2x)}}}