Question

Can anyone help me with this geometry proof

Answer 1

Answer:

m∠3 = 57° → proved down

Step-by-step explanation:

The given is:

• Lines $l_{1}$ and $l_{2}$
• Lines $t_{1}$ and $t_{2}$
• m∠1 = 123°

We want to prove that m∠3 = 57°

∵  $l_{1}$ // $l_{2}$ and $t_{1}$ is the transversal → given

∴ m∠1 = m∠2 → corresponding angles

∵ m∠1 = 123° → given

∴ m∠2 = 123° → equality of two corresponding angles

∵ $t_{1}$ // $t_{2}$ and $l_{2}$ 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