Match the reasons with the statements in the proof to prove that lines l and m are parallel, given that m2 = 122° and m3 = 58° Given: m2 = 122° and m3 = 58° Prove: l || m 1. m2 = 122° andm3 = 58° Subtraction Property of Equality 2. 3 and 5 are supplementary angles Second Substitution 3. m3 + m5 = 180° Given 4. 58° + m5 = 180° Exterior Sides in Opposite Rays 5. m5 = 122° If corresponding angles are equal, then lines are parallel. 6. m2 = m5 Definition of Supplementary Angles 7. l || m First Substitution

The reasons with the proof that the lines l and m are parallel is elaborated with the correct match. the statements in the proof to prove that the lines l and m are parallel, various information is given regarding two line in the question, if we arrange them with their correct order, the match can be obtained.

Given information:

The various information is given regarding two line in the question, if we arrange them with their correct match the following match can be obtained:

The correct match is given as:

Given - m\(\angle 2\) \(=122^o\) and m\(\angle3=58^o\)

Exterior sides in opposite rays - \(\angle 3\) and \(\angle 5\)supplementary angles

Definition of supplementary angle - \(\angle3+\angle5=180^o\)

Substitution - \(58^o+m\angle5=180^o\)

subtraction property - \(m\angle5=122^o\)

\(m\angle2 =m\angle5\) - Substitution

l║m - if corresponding angles are equal, then lines are parallel.

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