Four angles share a vertex: m∠1=32° , m∠2=148° , m∠3=32° , and m∠4=148° . Which angle is a vertical angle with ∠2 ?

The vertical angle with ∠2 would be ∠4.

Two intersecting lines create four angles, numbered 1, 2, 3, and 4, where ∠4 is adjacent to ∠1 and ∠3 , and m∠2=110° . Which other angle has a measure that is also equal to 110° ?

The other angle that has a measure equal to 110° would be ∠3 since ∠3 and ∠2 are adjacent angles formed by the intersecting lines, which means they share a vertex and a side. Therefore, if ∠2 has a measure of 110°, ∠3 would also have a measure of 110°.

no its 4

Apologies for the previous incorrect response. You are right.

If ∠4 is adjacent to ∠1 and ∠3, and we know that ∠2 has a measure of 110°, then ∠4 must have the same measure as ∠2, which is also 110°. Therefore, ∠4 has a measure of 110°.