Question

Which statements about the diagram are true? Check all that apply.

Answer 1

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

$x = 63\\z = 117\\x + z = 180$