Answer/Step-by-step explanation:
Given, m<2 = 63°; m<9 = 105°, and line a is parallel to b:
a. m<1 + m<2 = m<9 (alternate exterior angles are congruent)
m<1 + 63° = 105° (substitution)
Subtract 63 from each side
m<1 = 105° - 63°
m<1 = 42°
b. m<3 + m<2 + m<1 = 180° (angles in a straight line)
m<3 + 63° + 42° = 180° (substitution)
m<3 + 105° = 180°
m<3 = 180° - 105°
m<3 = 75°
c. m<4 = m<1 (vertical angles are congruent)
m<4 = 42°
d. m<5 = m<2 (vertical angles are congruent)
m<5 = 63°
e. m<6 = m<3 (vertical angles are congruent)
m<6 = 75°
f. m<7 = m<9 (vertical angles are congruent)
m<7 = 105°
g. m<8 = m<6 (alternate interior angles are congruent)
m<8 = 75°
h. m<10 = m<8 (vertical angles are congruent)
m<8 = 75°
i. m<11 = m<4 (alternate interior angles)
m<11 = 42°
j. m<12 = 180° - m<11 (linear pair theorem)
m<12 = 180° - 42° (substitution)
m<12 = 138°
k. m<13 = m<11 (vertical angles are congruent)
m<13 = 42° (substitution)
l. m<14 = m<12 (vertical angles are congruent)
m<14 = 138°