If a||b m<2=63 and m<9=105 find the measure of each missing angle

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°

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