When two angles are a linear pair, the sum of their measures is 180°:
∡1 + ∡ 2 = 180°
Substituting the expressions for the angles, you get:
5y − 8 + 12 + 6y = 180
Solve for y:
11y = 176
y = 176/11
Now, substitute this value in the expression for ∠2, which is the one we are interested in:
∡2 = 12 + 6y = 12 + 6×(176/11) = 108°
When two angles are vertical angles, it means that they share the same vertex and they have the same measure, therefore:
∡3 = ∡2 = 108°
Hence, the correct answer is C) 108°.