Answer:
Part a)
1) m<9 and m<28 is a pair of alternate interior angles that are congruent
2) m<9 and m<16 is a pair of alternate interior angles that are not congruent
Part b)
1) m<13 and m<22 is a pair of alternate exterior angles that are congruent
2) m<13 and m<24 is a pair of alternate exterior angles that are not congruent
Part c)
1) m<6 and m<30 is a pair of corresponding angles that are congruent
2) m<6 and m<18 is a pair of corresponding angles that are not congruent
Step-by-step explanation:
Part a) Using line e as the transversal, name one pair of alternate interior angles that are congruent and one pair of alternate interior angles that are not congruent
1) Using parallel lines a and c and transversal line e
[tex]m<9=m<28[/tex]
so
m<9 and m<28 is a pair of alternate interior angles that are congruent
2) Using lines a and b and transversal line e
[tex]m<9 \neq m<16[/tex]
so
m<9 and m<16 is a pair of alternate interior angles that are not congruent
Part b) Using line b as the transversal, name one pair of alternate exterior angles that are congruent and one pair of alternate exterior angles that are not congruent
1) Using parallel lines d and e and transversal line b
[tex]m<13=m<22[/tex]
so
m<13 and m<22 is a pair of alternate exterior angles that are congruent
2) Using lines d and f and transversal line b
[tex]m<13 \neq m<24[/tex]
so
m<13 and m<24 is a pair of alternate exterior angles that are not congruent
Part c) Using line f as the transversal, name one pair of corresponding angles that are congruent and one pair of corresponding angles that are not congruent
1) Using parallel lines a and c and transversal line f
[tex]m<6=m<30[/tex]
so
m<6 and m<30 is a pair of corresponding angles that are congruent
2) Using lines a and b and transversal line f
[tex]m<6 \neq m<18[/tex]
so
m<6 and m<18 is a pair of corresponding angles that are not congruent
