Answer:
Option A.
Step-by-step explanation:
Given information: m║n, [tex]m\angle 4=(5a+10)^{\circ}[/tex] and [tex]m\angle 6=(3a+10)^{\circ}[/tex].
If a transversal line intersect two parallel lines, then the interior angles on the same sides are supplementary angles. It means their sum is 180.
From the given figure it is clear that angle 4 angle 6 are interior angles on the same side. So, angle 4 and 6 are supplementary angles.
[tex]m\angle 4+m\angle 6=180^{\circ}[/tex]
[tex](5a+10)+(3a+10)=180[/tex]
On combining like terms we get
[tex](5a+3a)+(10+10)=180[/tex]
[tex]8a+20=180[/tex]
Subtract 20 from both sides.
[tex]8a+20-20=180-20[/tex]
[tex]8a=160[/tex]
Divide both sides by 8.
[tex]a=20[/tex]
The value of a is 20.
[tex]m\angle 4=(5a+10)^{\circ}\Rightarrow 5(20)+10)^{\circ}=110^{\circ}[/tex]
Therefore, the correct option is A.
