Answer:
x = 46
Step-by-step explanation:
First, it seems possible to find y, as there are two vertical angles, which are congruent, or equal:
2y + 6 = 8y - 102
Add 102 to each side:
2y + 108 = 8y
Subtract 2y from each side:
108 = 6y
Divide each side by 6:
18 = y
Now lets substitute this in to one of the equations using y:
2y + 6
2 ( 18 ) + 6
36 + 6
42
Now use this angle and the supplement of the angle (the angle next to it) because they add up to 180 degrees:
42 + ? = 180
180 - 42 = ?
180 - 42 = 138
Why do we need this?
Now we have the vertical angle that is equal to the equation with x, which we can solve now:
3x = 138
Divide each side by 3:
x = 46
You can check this by substituting the two values in for two equations to see if they add up to 180:
2y + 6 + 3x = 180
2 ( 18 ) + 6 + 3 ( 46 ) = 180
36 + 6 + 138 = 180
42 + 138 = 180
180 = 180
