[tex]\tt Step-by-step~explanation:[/tex]
Since ∠4 and ∠8 are corresponding angles, then that means they are congruent.
PART 1
[tex]\tt Step~1:[/tex]
m∠4: (12x + 3)
m∠8: (15x - 15)
Since they have the same measure, we can set up the equation like this:
[tex]\tt (12x+3)=(15x-15)[/tex]
[tex]\tt Step~2:[/tex]
Our goal is to isolate the variable x. To do that, we need to move everything to one side and keep x on its own on one side of the equation.
Let's subtract 12x from both sides to move it to the right.
[tex]\tt 12x(-12x)+3=15x(-12x)-15\\3=3x-15[/tex]
[tex]\tt Step~3:[/tex]
Then, we add 15 from the right side and on the left side of the equation.
[tex]\tt 3(+15)=3x-15(+15)\\18=3x[/tex]
[tex]\tt Step~4:[/tex]
Finally, we divide both sides by 3 to get our value for x.
[tex]\tt\frac{3x}{3}=x\\\frac{18}{3} =6\\x=6[/tex]
PART 2
[tex]\tt Step~5:[/tex]
Now, we have to plug in x in the expression for m4.
[tex]\tt 12(6)+3\\72+3\\75[/tex]
[tex]\large\boxed{\tt Our~final~answer:~m~4=75}[/tex]
**The numbers in parenthesis with a + or - tells you to add or subtract ONLY HERE. If you see this in another problem, they are most likely telling you to multiply.
