Question

I have two proof questions and I don't really know how to do them.

Answer 1

$\angle1\cong\angle2$ corresponding angles, therefore

m∠1 = m∠2 → m∠2 = 130°

$\angle2\cong\angle3$ vertical angles, therefore

m∠2 = m∠3 → m∠3 = 130°

If ∠1 and ∠2 are complementary, then m∠1 + m∠2 = 90°.

If ∠2 and ∠3 are complementary, then m∠2 + m∠3 = 90°

Therfore

$m\angle1 + m\angle2 = m\angle2 + m\angle3\qquad|\text{subtract}\ m\angle2\ \text{ from both sides}\\\\m\angle1 = m\angle3\to\angle1\cong\angle3$