Answer:
[tex]m\angle 2=95^{\circ}[/tex]
Step-by-step explanation:
It is given that ∠1 and ∠2 are a linear pair. So, there sum is 180 degrees.
[tex]m\angle 1+m\angle 2=180^{\circ}[/tex] ...(1)
∠2 and ∠3 are vertical angles. So, both are equal.
[tex]m\angle 2=m\angle 3[/tex] ...(2)
From (1) and (2), we get
[tex]m\angle 1+m\angle 3=180^{\circ}[/tex]
Substitute [tex]m\angle 1=(3y+10)^{\circ}[/tex] and [tex]m\angle 3=(5y-30)^{\circ}[/tex] in the above equation.
[tex](3y+10)^{\circ}+(5y-30)^{\circ}=180^{\circ}[/tex]
[tex](8y-20)^{\circ}=180^{\circ}[/tex]
[tex]8y-20=180[/tex]
[tex]8y=180+20[/tex]
Divide both sides by 8.
[tex]y=\dfrac{200}{8}[/tex]
[tex]y=25[/tex]
The value of y is 25.
Using equation (2), we get
[tex]m\angle 2=m\angle 3=(5y-30)^{\circ}[/tex]
Substitute y=25.
[tex]m\angle 2=(5(25)-30)^{\circ}[/tex]
[tex]m\angle 2=(125-30)^{\circ}[/tex]
[tex]m\angle 2=95^{\circ}[/tex]
Therefore, [tex]m\angle 2=95^{\circ}[/tex].
