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2 answers:
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Answer:
m∠3 = 57° → proved down
Step-by-step explanation:
The given is:
- Lines
and
- Lines
and
- m∠1 = 123°
We want to prove that m∠3 = 57°
∵ //
and
is the transversal → given
∴ m∠1 = m∠2 → corresponding angles
∵ m∠1 = 123° → given
∴ m∠2 = 123° → equality of two corresponding angles
∵ //
and
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