m∠IKL = 59°, given
m∠EIJ = 59°, corresponding angle theorem (If two parallel lines are cut by a transversal, then
corresponding angles are congruent.)
m∠EIJ + m∠IJG = 180°, Consecutive Interior Angle Theorem (If two parallel lines are cut by a transversal, then, interior angles on the same side of the transversal are supplementary.
59° + m∠IJG = 180°, substitution
m∠IJG = 180° - 59° , subtraction property of equality
m∠IJG = 121°, simplify
