∠1 and ​ ∠2 ​ are a linear pair, and ​ ∠2 ​ and ​ ∠3 ​ are vertical angles. m∠1=(5y−8)∘ and ​ m∠2=(12+6y)∘ . What is m∠3 ? A.16° B.72° C.108° D.132°

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°.