Answer/Step-by-step explanation:
Given:
m<3 = 83°
The following are the angle measures of the seven angles including the justification of each answer.
m<1 = m<3 (corresponding angles are congruent)
m<1 = 83° (substitution)
m<2 + m<3 = 180° (same side consecutive interior angles are supplementary)
m<2 = 180° - m<3 (Subtraction property of equality)
m<2 = 180 - 83
m<2 = 97°
m<4 + m<3 = 180° (linear pair)
m<4 = 180 - m<3 (Subtraction property of equality)
m<4 = 180 - 83 (substitution)
m<4 = 97°
m<5 = m<3 (vertical angles are congruent)
m<5 = 83°
m<6 = 180° - m<3 (linear pair theorem)
m<6 = 180 - 83°
m<6 = 97°
m<7 = m<3 (alternate interior angles are congruent)
m<7 = 83°
m<8 = m<6 (corresponding angles are congruent)
m<8 = 97°
