Question

Lines b and c are parallel.

What is the measure of 6?
a) m6 = 45°
b) m6 = 54°
c) m6 = 117°
d) m6 = 126°

Answer 1

the answer should be m angle 6 = 54°

Answer 2

we know that

a) By corresponding angles

m∠6=m∠2

b) By vertical angles

m∠6=
`(5x+9)\°`

so

m∠2=
`(5x+9)\°` --------> equation
`1`

c) By supplementary angles

`(13x+9)\°`+m∠2=
`180\°` --------> equation
`2`

substitute equation
`1` in equation
`2`

`(13x+9)\°+(5x+9)\°=180\°`

`(18x+18)\°=180\°`

`18x=180-18`

`x=9\°`

Find m∠6

m∠6=
`(5*9+9)\°`

m∠6=
`54\°`

therefore

the answer is

the measure of the angle 6 is
`54\°`