Respuesta :

nobrains
You got the answer y=78 by substituting x=20 into the top angle, 3x+18.
But the angle 3x+18 is not equal to the angle with the y variable.
They are supplementary angles (equal 180) but are not necessarily equal.
The angle that equals 2(y+6) is the angle opposite to it, 5x+2 (Vertical angle theorem).
So you should have substituted 20 into 5x+2
AL2006

You did the first step correctly ... even admirably !
You zeroed in on finding 'x' with laser-like precision, and
you knocked it out of the park.
Then, from there ... you fell off the deep end.

There's no reason that  (3x + 18)  has to be equal to 2(y+6).
In fact, they add up to 180°, so you could have used that
and solved for 'y'.

BUT ... (5x + 2) and 2(y+6) are "vertical angles", and THEY
are equal.

So   2 (y+6) = 5x + 2

       2 (y+6) = 102

          (y+6) = 51

           y       = 45 .