Question

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

x = 63


y = 47


z = 117


y + z = 180


x + z = 180

Answer 1

the answer is

x = 63

z = 117

x + z =180

Explanation:

Answer 2

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`