[tex]\angle1\cong\angle2[/tex] corresponding angles, therefore
m∠1 = m∠2 → m∠2 = 130°
[tex]\angle2\cong\angle3[/tex] 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
[tex]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[/tex]
