Statements
case 1) x = 63
we know that
m∠x°=\(63\)°-------> by corresponding angles
therefore
the statement case 1) is True
case 2) y = 47
we know that
\(47+x+y=180\\y=180-x-47\\y=180-63-47\\ y=70\ degrees\)
therefore
the statement case 2) is False
case 3) z = 117
we know that
\(z+63=180\) --------> by supplementary angles
\(z=180-63\\z=117\ degrees\)
therefore
the statement case 3) is True
case 4) y + z = 180
we know that
\(y=70\\ z=117\\ y+z=187\)
therefore
the statement case 4) is False
case 5) x + z = 180
we know that
\(x=63\\ z=117\\ y+z=180\)
therefore
the statement case 5) is True
Hence
the answer is
\(x = 63\\z = 117\\x + z = 180\)
