Question

Could anyone help me

Answer 1

Answer:

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) $m\angle 12=55\°$

Step-by-step 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]