Both lines w and v are parallel.
They are intersected by the lines p and q forming several angles.
Let's start with the angles formed between w, v, and p
We know that m∠9=80º
1)
m∠9 and m∠10 are a linear pair over line "p", linear pairs are adjacent supplementary angles, which means that they add up to 180º
Knowing this we can calculate the value of m∠10 as follows:
[tex]\begin{gathered} m\angle9+m\angle10=180 \\ m\angle10=180-m\angle9 \\ m\angle10=180-80 \\ m\angle10=100º \end{gathered}[/tex]
2)
Angles m∠2 and m∠10 are corresponding angles, if you see the lines between them are F shaped
Corresponding angles are congruent, so that
[tex]m\angle10=m\angle2=100º[/tex]
m∠2 measures 100º
