First of all, we know that a line is 180°. This means if we add the angles of 61°, 57°, and angle y, we should get 180°.
[tex]\sf 61\textdegree +57\textdegree+y=180\textdegree[/tex]
Simplify:
[tex]\sf 118\textdegree +y=180\textdegree[/tex]
Subtract 118° to both sides:
[tex]\sf y=62\textdegree[/tex]
We also know that all three angles of a triangle add up to 180°. So we have:
[tex]\sf 67\textdegree+62\textdegree +x=180\textdegree[/tex]
Simplify:
[tex]\sf 129\textdegree +x=180\textdegree[/tex]
Subtract 129° to both sides:
[tex]\sf x=\boxed{\sf 51\textdegree}[/tex]
