Solution/Step-by-step breakdown:
Information provided:
m<9 = 97°
m<12 = 114°
a. m<1 = m<9 because they are corresponding angles, which are equal.
m<1 = 97° (using substitution)
b. m<2 + m<1 = 180° (since they form a linear pair)
m<2 + 97° = 180° (substitute the value)
m<2 = 180 - 97 (subtracting 97 from both sides)
m<2 = 83°
c. m<3 = m<11 (as they are corresponding angles)
m<11 + m<12 = 180° (linear pair)
m<11 + 114° = 180° (substituting the known angle)
m<11 = 180 - 114
m<11 = 66°
m<3 = m<11 = 66°
d. m<4 + m<3 = 180° (linear pair)
m<4 + 66° = 180° (substituting the known angle)
m<4 = 180 - 66
m<4 = 114°
e. m<5 = m<2 as vertical angles are equal.
m<5 = 83° (using substitution)
f. m<6 = m<1 (vertical angles are equal)
m<6 = 97° (using substitution)
g. m<7 = m<4 (as vertical angles are equal)
m<7 = 114° (using substitution)
h. m<8 = m<3 (due to vertical angles being equal)
m<8 = 66° (using substitution)
i. m<10 = m<2 (corresponding angles are equal)
m<10 = 83° (using substitution)
j. m<11 = m<3 (because they are vertical angles)
m<11 = 66° (using substitution)
k. m<13 = m<5 (corresponding angles)
m<13 = 83° (applying substitution)
l. m<14 = m<9 (as vertical angles)
m<14 = 97° (applying substitution)
m. m<15 = m<12 (as vertical angles)
m<15 = 114° (applying substitution)
n. m<16 = m<11 (because they are vertical angles)
m<16 = 66° (applying substitution)
approximately 0.00020