It is given in this question that angle 1 and angle 2 are linear pair .
LInear pair are those angles , whose sum is 180 degree.
That is sum of measurements of angle 1 and angle 2 must be 180 degree. That is
[tex]x-30+x+76=180[/tex]
Combining like terms
[tex]2x+46=180[/tex]
Subtracting 46 from both sides
[tex]2x = 134[/tex]
Dividing both sides by 2
[tex]x=67[/tex]
So the two angles are
[tex]\angle 1 = 67-30=37 degree
\\
\angle 2 = 67+76= 143 degree[/tex]
