5.03 Quiz Parallel Lines And Transversals

Question: In this figure, AB∥CD and m∠1=110°.

What is m∠5?

Answer: m∠5= 110

Question: In Quadrilateral ABCD , AB∥CD and m∠2=35°.

What is m∠5?

Answer: m∠5= 35

Question: Given a∥b , and c is not parallel to a or b, which statements must be true?

Answer: m∠4=m∠5

m∠1=m∠5

Question: In this figure, AB∥CD and m∠6=75°.

What is m∠3?

Answer: m∠3= 105

Question: Given: m∥nm∠3=120°

Prove: m∠8=60°

Answer: m∥nm∠3=120° ​ → given

∠5≅∠3 → alternate interior angles theorem

m∠5=m∠3 → angle congruence postulate

m∠5=120° → substitution property of equality

m∠8+m∠5=180° → linear pair postulate

m∠8+120°=180° → substitution property of equality

​ m∠8=60° ​ → subtraction property of equality