Answer/Step-by-step explanation:
Given:
m<9 = 97°
m<12 = 114°
a. m<1 = m<9 (both angles are corresponding angles. Corresponding angles are congruent)
m<1 = 97° (substitution)
b. m<2 + m<1 = 180° (linear pair)
m<2 + 97° = 180° (substitution)
m<2 = 180 - 97 (subtracting 97 from both sides)
m<2 = 83°
c. m<3 = m<11 (corresponding angles)
m<11 + m<12 = 180° (linear pair)
m<11 + 114° = 180° (substitution)
m<11 = 180 - 114
m<11 = 66°
m<3 = m<11 = 66°
d. m<4 + m<3 = 180° (linear pair)
m<4 + 66° = 180° (substitution)
m<4 = 180 - 66
m<4 = 114°
e. m<5 = m<2 (vertical angles are congruent)
m<5 = 83° (substitution)
f. m<6 = m<1 (vertical angles are congruent)
m<6 = 97° (substitution)
g. m<7 = m<4 (vertical angles are congruent)
m<7 = 114° (substitution)
h. m<8 = m<3 (vertical angles are congruent)
m<8 = 66° (substitution)
i. m<10 = m<2 (corresponding angles are congruent)
m<10 = 83° (substitution)
j. m<11 = m<3 (vertical angles are congruent)
m<11 = 66° (substitution)
k. m<13 = m<5 (corresponding angles)
m<13 = 83° (substitution)
l. m<14 = m<9 (vertical angles)
m<14 = 97° (substitution)
m. m<15 = m<12 (vertical angles)
m<15 = 114° (substitution)
n. m<16 = m<11 (vertical angles)
m<16 = 66° (substitution)
