Question

Could anyone help me

Answer 1

1)
`m\angle 7 =65\°`

2)
`m\angle 4=115\°`

3)
`m\angle 6=115\°`

4)
`m\angle 1=65\°`

5)
`m\angle 16=60\°`

6)
`m\angle 18=60\°`

7)
`m\angle 21=120\°`

8)
`m\angle 10=55\°`

9)
`m\angle 11=125\°`

10)
`m\angle 12=55\°`

Explanation:

Given:

`e\parallel m` and
`p\ and\ q` are traversals.

`m\angle 3=65\°`

`m\angle 15 =120\°`

1)
`m\angle 7 = m\angle 3 =65\°` [corresponding angles]

2)
`m\angle 4= 180\°-m\angle 3 =180\°-65\°=115\°` [As
`m\angle 4+m\angle 3=180\°` forming a linear pair]

3)
`m\angle 6 = m\angle 4 =115\°` [alternate exterior angles]

4)
`m\angle 1 = m\angle 3 =65\°` [vertical angles]

5)
`m\angle 16= 180\°-m\angle 15 =180\°-120\°=60\°` [As
`m\angle 15+m\angle 16=180\°` forming a linear pair]

6)
`m\angle 18 = m\angle 16 =60\°` [alternate interior angles]

7)
`m\angle 21 = m\angle 15 =120\°` [alternate exterior angles]

`m\angle 14 = m\angle 16 =60\°` [vertical angles]

`m\angle 12+m\angle 7+m\angle 14=180\°` [Angle sum of triangle=180°]

`m\angle 12=180\°-65\°-60\°=55\°`[Plugging angle values in the above relation and solving for
`m\angle 12`

8)
`m\angle 10 = m\angle 12 =55\°` [Vertical angles]

9)
`m\angle 11= 180\°-m\angle 10 =180\°-55\°=125\°` [As
`m\angle 11+m\angle 10=180\°` forming a linear pair]

10)
`m\angle 12 = m\angle 10 =55\°` [Vertical angles]