Answer:
[tex]\boxed {\boxed {\sf v=9}}[/tex]
Step-by-step explanation:
In the diagram, there are 2 angles: 105° and (8v+3)°. They are on a straight line together, so they are supplementary angles. They must add to 180 degrees. We can set up an equation.
[tex]105 + (8v+3) = 180[/tex]
We are solving for v, so we must isolate the variable. First, we can rearrange the right side and combine the like terms (the constants without a variable).
[tex]105 +8v+3= 180 \\8v + (105+3) = 180 \\8v + 108= 180[/tex]
108 is being added to 8v. The inverse operation of addition is subtraction. Subtract 108 from both sides of the equation.
[tex]8v+108-108= 180-108 \\8v= 180-108 \\8v=72[/tex]
v is being multiplied by 8. The inverse operation of multiplication is division. Divide both sides by 8.
[tex]\frac {8v}{8}= \frac{72}{8}\\[/tex]
[tex]v= \frac{72}{8}[/tex]
[tex]v=9[/tex]
v is equal to 9.
