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