Answer:
m∠3 = 57° → proved down
Step-by-step explanation:
The given is:
- Lines [tex]l_{1}[/tex] and [tex]l_{2}[/tex]
- Lines [tex]t_{1}[/tex] and [tex]t_{2}[/tex]
- m∠1 = 123°
We want to prove that m∠3 = 57°
∵ [tex]l_{1}[/tex] // [tex]l_{2}[/tex] and [tex]t_{1}[/tex] is the transversal → given
∴ m∠1 = m∠2 → corresponding angles
∵ m∠1 = 123° → given
∴ m∠2 = 123° → equality of two corresponding angles
∵ [tex]t_{1}[/tex] // [tex]t_{2}[/tex] and [tex]l_{2}[/tex] is the transversal → given
∴ m∠2 + m∠3 = 180° → interior supplementary angles
∵ m∠2 = 123° → proved
∴ 123 + m∠3 = 180 → subtract 123 from both sides
∴ m∠3 = 57° → inverse addition property
